OpenTSTOOL User Manual - Third Institute of Physics

OpenTSTOOL User Manual - Third Institute of Physics
OpenTSTOOL User Manual
Version 1.2 (2/2009)
Christian Merkwirth
Ulrich Parlitz
Immo Wedekind
David Engster
Werner Lauterborn
Drittes Physikalisches Institut
Universit¨at G¨ottingen
Contact: [email protected]
2
Contents
1 At a glance
7
2 Download and Installation
9
2.1
Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.1.1
Installation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.1.2
Global installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.1.3
Deinstalling TSTOOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.2
First Steps
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
Compiling mex files
10
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
Problems with compiling mex files . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.4
Pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.5
Copyright notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.3.1
3 First Steps
3.1
15
Example analysis of a time-series from a chaotic Colpitts oscillator . . . . . . . . . . .
4 Nearest Neighbors Searching
15
19
4.1
Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
4.2
Approximate nearest neighbors searching . . . . . . . . . . . . . . . . . . . . . . . . .
19
4.3
Range searching
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
4.4
Matlab mex-functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
4.4.1
nn prepare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
4.4.2
nn search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
4.4.3
range search
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
4.5
Example session
5 Handling the Graphical User Interface
25
5.1
Filelist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
5.2
Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
5.3
Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
5.3.1
26
Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
5.3.2
Methods I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
5.3.3
Methods II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
5.3.4
Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
5.3.5
Modify
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
5.3.6
Macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
5.3.7
Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
5.3.8
Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
5.3.9
View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
6 Mex-Function Reference
33
6.1
akimaspline - Cubic spline interpolation using Akima splines . . . . . . . . . . . . . .
33
6.2
amutual - compute auto mutual information function
. . . . . . . . . . . . . . . . . .
34
6.3
baker - Generate Baker time-series . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
6.4
boxcount - Classical boxcounting algorithm . . . . . . . . . . . . . . . . . . . . . . . .
35
6.5
cao - Determine minimum embedding dimension by Cao’s method . . . . . . . . . . .
35
6.6
chaosys - integrate dynamical system given by a set of ordinary differential equations
36
6.7
corrsum - Computation of the correlation sum . . . . . . . . . . . . . . . . . . . . . .
38
6.8
corrsum2 - Computation of the correlation sum . . . . . . . . . . . . . . . . . . . . . .
39
6.9
fnearneigh - Fast nearest neighbor search . . . . . . . . . . . . . . . . . . . . . . . . .
40
6.10 gendimest - Estimate generalized dimension spectrum . . . . . . . . . . . . . . . . . .
41
6.11 henon - Generate henon time-series . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
6.12 largelyap - Compute separation of nearby trajectories . . . . . . . . . . . . . . . . .
42
6.13 nn prepare - Do nearest neighbor preprocessing . . . . . . . . . . . . . . . . . . . . .
43
6.14 nn search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
6.15 predict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
6.16 range search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
6.17 return time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
6.18 takens estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
6.19 tentmap - Generate tentmap time-series . . . . . . . . . . . . . . . . . . . . . . . . . .
47
6.20 Class signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
6.20.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
6.20.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
6.20.3 Member functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
6.21 Class description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
6.21.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
6.21.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
6.21.3 Member functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
6.22 Class core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
4
6.22.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
6.22.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
6.22.3 Member functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
6.23 Class achse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
6.23.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
6.23.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
6.23.3 Member functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
6.24 Class unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
6.24.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
6.24.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
6.24.3 Member functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
6.25 Class list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
6.25.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
6.25.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
6.25.3 Member functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
7 Frequently asked questions
93
7.1
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
7.2
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
7.2.1
Introduction and general information . . . . . . . . . . . . . . . . . . . . . . . .
94
7.2.2
Installation of TSTOOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
7.2.3
Working with TSTOOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
7.2.4
Extending TSTOOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
7.2.5
Miscellaneous questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
7.2.6
Frequently encountered errors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
5
Chapter 1
At a glance
What is TSTOOL ?
TSTOOL is a software package for signal processing with emphasis on nonlinear time-series analysis.
Objectives
• Implement existing algorithms for nonlinear time-series analysis
• Develop new methods for specific data analysis problems
• Create an expandable platform for signal processing
Implementation
The package is written partly in Matlab and partly in C++.
Advantages of Matlab are :
• Reduced code development time
• Extensive collection of intrinsic mathmatical functions
• Excellent graphic capabilities
• High portability from Unix to Windows NT and other platforms
C++ is used for computationally demanding algorithms.
Graphical user interface
A graphical user interface (GUI) gives access to the underlying signal processing commands. Parameters for the commands are set via dialog windows.
7
Chapter 2
Download and Installation
2.1
Installation
Unpack the compressed TSTOOL distribution into a directory, e.g C:\Program Files on Windows,
/usr/local on Unix.
This can be done with an unpacking tool like Winzip if you are working with Windows, or gzip -dc
filename.tgz | tar -xvf - if you are working with Unix.
After unpacking you will get a new directory named OpenTSTOOL which should now contain:
• tstoolInit.m - script that calls settspath.m if necessary
• settspath.m - script that does path settings
• tstoolbox - the directory that contains all TSTOOL functions, compiled mex files etc.
• mex-dev - Source code of the C++ parts of TSTOOL
• Doc - HTML/PDF Documentation
• info.xml, tstoolicon.gif - Files for the Matlab start menu
• gpl.txt - Gnu General Public License
Important note for Windows users: If you want to use the pre-compiled mex-files which ship
with OpenTSTOOL, you will probably have to install the Visual C++ 2008 run-time libraries, which
can be downloaded from the Microsoft web site. As of the writing of this document, the URLs for
these packages are
http://www.microsoft.com/downloads/details.aspx?FamilyID=9b2da534-3e03-4391-8a4d-074b9f2bc1bf
for 32bit and
http://www.microsoft.com/downloads/details.aspx?familyid=bd2a6171-e2d6-4230-b809-9a8d7548c1b6
for 64bit. If these URLs are no longer valid, just search for “Microsoft Visual C++ 2008 Redistributable Package” and “x86” or “x64” for 32bit and 64bit, respectively.
If you do not have these run-time libraries installed, you will get the following error message when
trying to run a mex-file: “This application has failed to start because the application configuration is
incorrect.”
9
2.1.1
Installation methods
The simplest way to invoke OpenTSTOOL is to start Matlab and change to the OpenTSTOOL directory
(using the GUI or the cd command). Once you have entered that directory, you should see the
OpenTSTOOL toolbox in your Matlab Start menu under the item Toolboxes, and you can start the
graphical user interface from there. Note that TSTOOL is not really installed yet, so that after
restarting Matlab you will have to enter the OpenTSTOOL directory again before you will be able to
use the toolbox.
If you want to install OpenTSTOOL permanently, the directories from the toolbox must be in the
Matlab path. There are several methods to include these directories, depending on you having full
control over the Matlab installation or using a network wide installation as a normal user with reduced
privileges.
• If you have full control over the installation: Enter the OpenTSTOOL directory and choose the
item Installation under Toolboxes → OpenTSTool in the Matlab Start menu. It will install the
OpenTSTool directories in the Matlab search path and call the path tool. Now simply click save
to store the current path for future sessions.
• If you are working with a networked installation: Enter the path tool as just described in the
previous paragraph, but after you click on save, you will get an error which states that the path
could not be saved. Now, choose Yes to save the file pathdef.m in your userpath, which you can
see by calling the command userpath in the Matlab shell (on UNIX this is usually the directory
<HOMEDIR>/matlab or <HOMEDIR>/Documents/matlab. Create it if it does not yet exist). You
might have to set the environment variable MATLAB USE USERPATH to 1 to make this work.
• If don’t have a graphical display and are working with the shell : Enter the OpenTSTOOL
directory, call tstoolInit and then savepath.
• Another possibility is to create a file startup.m in your userpath (usually <HOMEDIR>/matlab
or <HOMEDIR>/Documents/matlab), containing the following lines:
addpath(’<full path to the OpenTSTOOL-Dir>’);
settspath(’<full path to the OpenTSTOOL-Dir>’);
Again, on UNIX systems you might have to set the environment variable MATLAB USE USERPATH
to 1 to make this work.
2.1.2
Global installation
Last but not least, if all users of a network wide matlab installation should have access to TSTOOL,
just insert the paths which are set by the script settspath in the global path from Matlab.
2.1.3
Deinstalling TSTOOL
If you want to deinstall TSTOOL, simply remove the OpenTSTOOL directory, start pathtool in Matlab
and remove every directory containing OpenTSTOOL. Then save the path for future sessions.
2.2
First Steps
1. Start Matlab
2. Install paths as described in 2.1.1.
3. Enter tsdemo on the Matlab console. This should start a short demo script.
10
4. Enter tsdemo2 on the Matlab console. This should run a second script that shows an analysis
of a chaotic signal.
5. Note that you can also start the demos through the Matlab Start menu.
6. Enter opentstool to start the graphical user interface for the TSTOOL package.
7. You can also access the manual any time through the OpenTSTOOL entry in the Matlab start
menu.
2.3
Compiling mex files
If you do not find appropriate pre-compiled mex files for your platform on our home page, you can
compile them yourself. You will need an installed C++ compiler for doing this; the C compiler that
ships with MATLAB (LCC) does not compile C++ code at all and will therefore not work.
• GNU/Linux : The free compiler suite gcc usually comes pre-installed with most distributions.
You will need at least version 3.4 or newer (check with gcc -v). Run mex -setup in MATLAB
and choose the gccopts.sh options file for compilation.
• Solaris: You can also use gcc, but the C++ compiler from Sun Forte Studio should also work
(Version 7 or newer). For using the latter, make sure the command cc runs the correct compiler
in the shell, call mex -setup in MATLAB and choose the system’s ANSI compiler.
• Mac OS X : The gcc suite is available through Apple’s XCode Developer Tools, which can be
downloaded from
http://developer.apple.com/TOOLS/xcode
(registration required). As for GNU/Linux, run mex -setup and choose gccopts.sh.
• Windows: Unfortunately, compiling mex files under Windows ist more difficult to do, since
each MATLAB version is pretty picky about which version of which compiler it supports. If
you happen to have Microsoft Visual C++ Professional, this should usually be detected by mex
-setup and it should compile the C++ files just fine. If you want to use the Express edition,
which you can download free of charge from Microsoft, usually only the newest MATLAB version
(currently 7.7) will support it directly. For older MATLAB versions, you will also have to install
the Microsoft Windows SDK for Windows Server 2008 and .NET Framework and copy some
files in the right places. Fortunately, there’s an tutorial for this, which you’ll find at
http://www.mathworks.com/matlabcentral/fileexchange/22689
Alternatively, like on Unix systems, you can install the free gcc compiler on Windows, which is
available under the name MinGW (minimalist gcc for Windows). Unfortunately, Matlab does
not officially support this compiler under Windows, so you cannot use it by simply calling mex
-setup. Instead, you can try to use the free tool GnuMex to create a proper compilation batch
file for you. Please visit the following web sites for details and downloads:
GnuMex: http://gnumex.sourceforge.net
MinGW: http://www.mingw.org
Note that GnuMex will currently not work on 64bit Windows systems out of the box!
After you have set up the mex tool, enter the subdirectory mex-dev and call makemex. This function
will compile all the necessary files and copy them into the tstoolbox/mex/<MEXEXT> subdirectory.
11
2.3.1
Problems with compiling mex files
Dependent on the version you are using, Matlab will support only a certain range of gcc compilers. If
you are using an unsupported gcc version, you will see a warning message like this during compilation:
Warning: You are using gcc version "X.X.X". The earliest gcc version supported
with mex is "Y.Y.Y". The latest version tested for use with mex is "Z.Z.Z".
To download a different version of gcc, visit http://gcc.gnu.org
While compiling with a newer gcc version often works despite the warning, you should still try to use
a gcc version which your version of Matlab supports.
On many Unix systems (especially most Linux distributions), more than one version of gcc is installed,
and often you can use one certain version by using an explicit command like gcc-X.Y. You can put the
appropriate command into the mexopts.sh file (instead of just gcc and g++), which Matlab created
for you during mex -setup. On Unix systems, it can be found in the directory .matlab/VERSION
under your home directory.
Another problem can occur due to Matlab coming with its own versions of the standard C/C++ and
gcc libraries (at least under Unix systems). This can lead to problems if your mex files were linked
against another C library installed on your system. You will typically get an error like the following
when calling such a mex file:
<MATLABROOT>/sys/os/glnx86/libgcc_s.so.1: version ‘GCC_4.2.0’ not
found (required by /usr/lib/libstdc++.so.6)
There exist basically two options for solving this problem. Note that as far as we know, both are not
officially supported by The Mathworks, but usually work nonetheless.
• First option:
move the files libstdc++*,
libgcc* and libg2c* from
<MATLABROOT>/sys/os/<SYSTEM> to another location, for example a subdirectory named
old. You will thereby enforce the libraries installed on your system. If you encounter problem
afterwards, simply move the libraries back and restart Matlab. Of course, you need control over
the Matlab installation for doing this.
• Second option: Set the environment variable LD PRELOAD to enforce usage of your installed
system libraries. For example, you may call Matlab the following way from the command line:
LD_PRELOAD=/usr/lib/libstdc++.so.6:/lib/libgcc_s.so.1 matlab
This option is a bit more cumbersome, but has the advantage that you can do this as normal
user. Note that this command is only an example; check your library directories for the correct
paths and file names.
2.4
Pitfalls
See also the FAQ (Frequently Asked Questions) 7!
1. As of TSTOOL version 1.2, the main function for creating the TSTOOL GUI is called
opentstool instead of tstool to avoid collision with the time series toolbox from The Mathworks.
2. When using Winzip, enable Use path information to make sure that subdirectories are created.
3. TSTOOL will not work with Matlab version prior to 6.5!
4. It’s not a good idea to place the TSTOOL distribution into the Matlab directory. We obtained reports about strange bugs occuring when the TSTOOL distribution is extracted into the
directory where the Matlab system is installed.
12
2.5
Copyright notice
TSTOOL falls unter the GNU General Public License. See gpl.txt in the OpenTSTOOL directory or
http://www.physik3.gwdg.de/tstool/gpl.txt. .
13
Chapter 3
First Steps
3.1
Example analysis of a time-series from a chaotic Colpitts
oscillator
In this section we briefly demonstrate basic steps for anaysing a chaotic time series. The methods
used will be explained ind maore detail in the following sections.
>> s = signal(’colpitts.dat’,’ascii’)
s = signal object
Dlens : 6001
X-Axis 1 : |
Name : colpitts
Type :
Attributes of data values :
|
Comment :
History :
17-Aug-1999 15:08:24 : Imported from ASCII file ’colpitts.dat’
By entering the above command line, the overloaded constructor for class signal was called. Giving a
filename as argument tells the constructor to load the datafile and convert it into a signal object. The
datafile ’colpitts.dat’ contains a time-series generated by an electronical Colpitts circuit that oscillates
chaotically.
To plot signal s, just issue the following command :
view(s);
15
Lets find a good choice for a delay-time by using the first minimum of the auto mutual information
function
a = amutual(s,32);
view(a);
the first minimum of the auto mutual information can be found at four. Now we need to know the
minimal embedding dimension for the colpitts signal. We use Cao’s method with a delay time of four,
a maximal dimension of eight, three nearest neighbors and 1000 reference points.
c = cao(s,8,4,3,1000);
view(c);
There’s a kink in the graph produced by Cao’s method at three. So now do a time-delay reconstruction
of the Colpitts signal with embedding dimension 3 and delay 4.
16
e = embed(s, 3, 4);
view(e);
What’s the correlation dimension of the reconstructed data set ? First let’s take a look at the scaling
of the correlation sum versus the radius (as log-log plot).
view(corrsum(e, -1, 0.05, 40, 32));
Next, we use the Takens estimator for the correlation dimension. It needs basically the same input
arguments as the function corrdim2.
>> takens_estimator(e, -1, 0.05, 40)
ans =
1.9483
And what about it’s largest Lyapunov exponent ? To estimate the largest Lyapunov exponent, we
take a look at the scaling of the prediction error.
view(largelyap(e, 1000, 300, 40, 2));
17
18
Chapter 4
Nearest Neighbors Searching
An integral part of a majority of methods for nonlinear time series analysis is searching for nearest
neighbors. The perfomance of these methods depends strongly of the perfomance of the employed
nearest neighbor algorithm. Thus, choosing an efficient nearest neighbor algorithm should be done
very carefully.
4.1
Definition
Definition : A set P of data points in D-dimensional space is given. Then we define the nearest
neighbor to some reference point q (also called query point) to be the point of data set P that has
the smallest distance to q (we don’t issue the problem of ambiguity at this point).The more general
task of finding more than one nearest neighbor is called k nearest neighbors problem. In general, the
reference point q is an arbitrarily located point, but it is also possible that q is itself a member of
data set P (as illustrated in the figure, where five neighbors to q (excluding self match) are found).
4.2
Approximate nearest neighbors searching
Approximate nearest neighbors algorithms report neighbors to the query point q with distances possibly greater than the true nearest neighbors distances. The maximal allowed relative error epsilon is
given as a parameter to the algorithm. For epsilon=0, the approximate search returns the true (exact)
nearest neighbor(s).
Computing exact nearest neighbors for data set with fractal dimension much higher than 6 seems to
be a very time-consuming task. Few algorithms seem to perform significantly better than a bruteforce computation of all distances. However, it has been shown that by computing nearest neighbors
approximately, it is possible to achieve significantly faster execution times with relatively small actual
errors in the reported distances.
19
4.3
Range searching
In the task of range searching, we ask for all points of data set P that have distance r or less from the
query point q. Sometimes range searching is called a fixed size approach, while k nearest neighbors
searching is called a fixed mass approach.
4.4
Matlab mex-functions
4.4.1
nn prepare
nn prepare does the preprocessing for a given data set pointset. The returned data structure atria
contains preprocessing information that is necessary to use nn search or range search.
Preprocessing and searching is divided into different mex-files to give the user the possibility to reuse the preprocessing data (contained in atria) when doing multiple searches on the same point set.
However, as soon as the underlying point set is changed or modified, one has to recompute atria for
the changed point set.
Syntax:
•
atria = nn_prepare(pointset)
•
atria = nn_prepare(pointset, metric)
•
atria = nn_prepare(pointset, metric, clustersize)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• metric - (optional) either ’euclidian’ or ’maximum’ (default is ’euclidian’)
• clustersize - (optional) threshold for clustering algorithm, defaults to 64
4.4.2
nn search
nn search does exact or approximate k-nearest neighbor queries to one or more query points. These
query points can be given explicitly or taken from the data set of points (see below).
Before one can use nn search, one has to call nn prepare to compute the preprocessing information.
However, as long as the input point set isn’t modified, the preprocessing information is valid and can
be re-used for multiple calls to nn search or range search.
Syntax:
20
•
[index, distance] = nn_search(pointset, atria, query_points, k)
•
[index, distance] = nn_search(pointset, atria, query_points, k, epsilon)
•
[index, distance] = nn_search(pointset, atria, query_indices, k, exclude)
• [index, distance] = nn_search(pointset, atria, query_indices, k,
exclude, epsilon)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• atria - output of nn prepare for pointset
• query points - a R by D double matrix containing the coordinates of the query points, organized as R points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• k - number of nearest neighbors to compute
• epsilon - (optional) relative error for approximate nearest neighbors queries, defaults to 0 (=
exact search)
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• index - a matrix of size R by k which contains the indices of the nearest neighbors. Each row
of index contains k indices of the nearest neighbors to the corresponding query point.
• distance - a matrix of size R by k which contains the distances of the nearest neighbors to the
corresponding query points, sorted in increasing order.
4.4.3
range search
The routine range search does a range search to one or more query points. These query points can
be given explicitly or taken from the data set of points (see below).
Before one can use range search, one has to call nn prepare to compute the preprocessing information. However, as long as the input point set isn’t modified, the preprocessing information is valid
and can be re-used for multiple calls to nn search or range search.
Syntax:
•
[count, neighbors] = range_search(pointset, atria, query_points, r)
•
[count, neighbors] = range_search(pointset, atria, query_indices, r, exclude)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
21
• query points - a R by D double matrix containing the coordinates of the query points, organized as R points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points
• r - range or search radius (r > 0)
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• count - a vector of length R contains the number of points within distance r to the corresponding
query point
• neighbors - a Matlab cell structure of size R by 2 which contains vectors of indices and vectors
of distances to the neighbors for each given query point. This output argument can not be stored
in a standard Matlab matrix because the number of neighbors within distance r is not the same
for all query points. The vectors if indices and distances for one query point have exactly the
length that is given in count. The values in the distances vectors are not sorted.
4.5
Example session
% create a 3-dimensional data set with 100000 points
pointset = rand(100000, 3);
% do the preprocessing for this point set
atria = nn_prepare(pointset, ’euclidian’);
% now search for 2 (exact) nearest neighbors, using points 1 to
% 10 as query points, excluding self-matches
[index, distance] = nn_search(pointset, atria, 1:10, 2, 0)
index =
5618
38209
54991
38429
4114
72121
13678
26022
86042
24830
96574
84549
60397
59732
76991
452
59332
16718
38436
44434
distance =
22
0.0101
0.0078
0.0132
0.0050
0.0087
0.0124
0.0129
0.0046
0.0101
0.0156
0.0175
0.0134
0.0167
0.0223
0.0097
0.0189
0.0168
0.0110
0.0103
0.0177
% now do a range search for radius 0.0224, using points 1 to 10 as
% query points, excluding self-matches
[count, neighbors] = range_search(pointset, atria, 1:10, 0.0224, 0)
count =
4
10
7
2
5
6
2
4
7
5
neighbors =
[1x4
[1x10
[1x7
[1x2
[1x5
[1x6
[1x2
[1x4
[1x7
[1x5
double]
double]
double]
double]
double]
double]
double]
double]
double]
double]
[1x4
[1x10
[1x7
[1x2
[1x5
[1x6
[1x2
[1x4
[1x7
[1x5
double]
double]
double]
double]
double]
double]
double]
double]
double]
double]
% let’s see the indices of the points that are within range to the first query point
neighbors{1,1}
ans =
56921
97100
96574
5618
% let’s see the corresponding distances of the points that are
% within range to the first query point
neighbors{1,2}
23
ans =
0.0176
0.0186
0.0175
0.0101
24
Chapter 5
Handling the Graphical User
Interface
With the Graphical User Interface (GUI) most of TSTOOLs methods are available without coping
with the command line syntax of every function.
To invoke the GUI simply type opentstool at the matlab command prompt. If you invoke the GUI
for the first time, you get informed that the GUI will generate a directory for temporary files. This
will reside at OpenTSTOOL/datafiles on Windows systems and at ~/.tstool on Unix systems.
First of all, how does the GUI looks like?
There are three parts:
• Filelist
• Figure
• Menubar
5.1
Filelist
Every loaded or generated signal shows its name in an own line, they arranged hierarchicaly. The
data of the signals is stored in seperated files in the directory generated at the first run.
To process a special method, click on one of the signals in the filelist an choose the method from the
menubar.
25
5.2
Figure
This figure can show you the signal you have choosen from the filelist. Normaly this feature is switched
off because of the time consumption especialy for large signals. To switch on this feature choose the
menu item Option-Instant View-Small Window.
5.3
Menus
5.3.1
Signal
All menu items in this menu have something to do with the filelist and the storage of the signals.
• Load
This menu item simply loads data into the GUI (more precise: load a signal and save it to the
temporary data directory). A line in the fileview will be added with its filename.
• Save
Write the marked signal in the fileview to disk.
• Import file from
Generate a signal from foreign formats like ASCII, Matlab Vector, Soundfiles etc. See signal
class constructor reference (6.20.3.66) for more information.
• Export file from
Write the marked signal in the fileview to disk in a foreign format. See signal/write reference
(6.20.3.83) for more information.
• Generate
This menu item can generate signals. See mex/chaosys reference (6.6).
• Audio playback
Plays a scalar signal as audio with the matlab function soundsc. If there is no sampling rate
set in the signal 8KHz will be used.
• Rescan
Normally all files with the correct extension in the temporary directory are displayed in the
filelist. For some reason it is possible that a signal is displayed in the filelist but doesnt exist (e.
g. an other process deleted this file) or some files missing in the filelist (e. g. if you simply copy
a signal file in the temporary directory without using the Load menu item). In such situation
use the Rescan menu item to let TSTOOL look up all files again correctly. This can take some
time on slow machines or large signal files. Simply restarting the GUI will not make a rescan!
• Remove entry
If you want to remove a filelist entry use this menu item or simply type Ctrl-d. The selected
filelist entry will disappear and the corresponding temporary file will be deleted.
• Show
A signal stores many information about the data. This information can be displayed by this
menu item.
• Edit
– Desired type of plot
Here you can choose the type of plot TSTOOL should use for your signal. See signal/view
reference (6.20.3.82) for additional information.
26
– Descriptive parameters
– Axes labels
– Comment text
5.3.2
Methods I
In this menu all methods with scalar input are grouped. Most of this methods invokes the underlying
TSTOOL-function directly and do not need addition explanations. To enter the parameters a dialog
box will be opened.
For some parameters there is a checkbox at the right side named ’in units’. Normally this parameter
is entered in the units of samples. When you switch on the checkbox you can also enter this parameters
in units of the first axis.
• Reconstruction
– Time-Delay vectors
see signal/embed (6.20.3.21)
– Minimum Embedding Dimension (Cao’s)
see signal/cao (6.20.3.9)
• Spectral
– FFT
see signal/fft (6.20.3.22)
– Periodogram
see signal/spec (6.20.3.68)
– Spectrogram
see signal/spec2 (6.20.3.69)
– Scalogram
see signal/scalogram (6.20.3.62)
• Derivative/Integration
– Integrate
see signal/int (6.20.3.33)
– Differentiate
see signal/diff (6.20.3.18)
• Correlation and more
– Auto Correlation
see signal/acf (6.20.3.2)
– Auto Mutual Information
see signal/amutual (6.20.3.4)
• Filter
– Moving Average
see signal/movav (6.20.3.44)
– Median Filter
see signal/medianfilt (6.20.3.40)
– Multiresolution Analysis
see signal/mutlires (6.20.3.45)
27
• Surrogate Data Generation
– Permutation of Samples
see signal/surrogate3 (6.20.3.74)
– Theiler Alg. I
see signal/surrogate1 (6.20.3.72)
– Theiler Alg. II
see signal/surrogate2 (6.20.3.73)
• Surrogate Data Test
– Time Reversibility
see signal/trev (6.20.3.80)
– Higher order moments
see signal/tc3 (6.20.3.78)
– Function
see signal/surrogate test (6.20.3.75)
• Prediction
– Local Constant
see signal/predict2 (6.20.3.55)
• Misc
– Squared Magnitude
see signal/power (6.20.3.53)
– Absolute Value
see signal/abs (6.20.3.1)
– Decibel Value
see signal/db (6.20.3.16)
– Histogram
see signal/histo (6.20.3.30)
5.3.3
Methods II
In this menu all methods with multivariate input signals are grouped.
• Decompositions
– PCA (Karhunen-Loeve)
see signal/pca (6.20.3.49)
– Archetypal Analysis
see signal/arch (6.20.3.7)
• Lyapunov Exponents
– Largest
see signal/largelyap (6.20.3.36)
• Fractal Dimensions
– Box Counting Approach
28
∗ Capacity Dimension D0
see signal/boxdim (6.20.3.8)
∗ Information dimension D1
see signal/infodim (6.20.3.31)
∗ Correlation dimension D2
see signal/corrdim (6.20.3.11)
– Correlation Sum Approach
∗ Correlation Sum D2 (GPA like approach)
see signal/corrsum (6.20.3.12)
∗ Correlation dimension D2 (fixed number of pairs)
see signal/corrsum2 (6.20.3.13)
∗ Takens Estimator D2
see signal/takens estimator (6.20.3.77)
– Nearest Neighbor Algorithms
∗ Information dimension D1 (NNK)
see signal/infodim2 (6.20.3.32)
∗ Fractal dimension spectrum
see signal/fracdims (6.20.3.27)
• Periodicity
– Return Times
see signal/return time (6.20.3.58)
– Reciprocal local density
see signal/localdensity (6.20.3.38)
• Modeling
– Polynom selection
see util/pauswahl
• Poincare Section
see signal/poincare (6.20.3.52)
• Prediction
– Local Constant
see signal/predict (6.20.3.54)
5.3.4
Utilities
Some useful information about the signals can be retrieved by functions in this menu.
• Minimum
see signal/min (6.20.3.42)
• Maximum
see signal/max (6.20.3.39)
• First Local Minimum
see signal/firstmin (6.20.3.25)
• First Local Maximum
see signal/firstmax (6.20.3.24)
29
• First Zero Crossing
see signal/firstzero (6.20.3.26)
• Mean
see mean (Matlab reference)
• Standard Deviation
see std (Matlab reference)
• RMS
root mean square
• Compare two Signals
Only the data values are compared. See core/compare (6.22.3.3)
5.3.5
Modify
• Cut
see signal/cut (6.20.3.15)
• Swap Dimensions
see signal/swap (6.20.3.76)
• Reverse
see signal/reverse (6.20.3.59)
• Interpolations
– Cubic Spline
see signal/upsample (6.20.3.81)
– Akima Spline
see signal/upsample (6.20.3.81)
– FFT Based
see signal/upsample (6.20.3.81)
• Normalize
– Center around Zero
see signal/center (6.20.3.10)
– Scale by Factor
see signal/scale (6.20.3.61)
– Fit to Interval
see signal/norm1 (6.20.3.47)
– Center and Divide by STD
see signal/norm2 (6.20.3.48)
– Remove Trend
see signal/trend (6.20.3.79)
– Transform to Rang Values
see signal/rang (6.20.3.56)
• Split Multichannel Signal
Splits up a n-channel signal in n signals by using signal/cut (6.20.3.15).
30
• Add two Signals
see signal/plus (6.20.3.51)
• Difference of two Signals
see signal/minus (6.20.3.43)
• Merge two Signals
see signal/merge (6.20.3.41)
5.3.6
Macro
TSTOOL records the processed commands for every signal. So TSTOOL knows how this signal is
modified and can generate a matlab script with processes the same commands to arbitrary signal.
The generated scripts will be saved in the directory scripts inside the directory for temporary files.
• Create Macro from Signal
Generate script named macro.m.
• Show/Edit Macro
• Rename Macro
Renamed macros will be displayed at the end of this menu after restart of TSTOOL.
• Apply Macro to Signal
Invoke macro.m with the selected signal.
• Apply Macro to all
Invoke macro.m with every loaded signal.
After the seperation line a list of all *.m-Files in the directory scripts is shown. Selecting one of
these menus apply the corresponding script to the actual selected signal.
5.3.7
Options
Here some settings can be edited. All these settings will be saved in the file tstool.mat in the
temporary data directory.
• Parameters
– Reconstruction Parameters
The default settings for the Reconstruction dialog box can be edited here (see menu Methods I - Reconstruction - Time Delay Vectors 5.3.2)
– Default Window Type
Used by FFT etc.
• File and Directory Options
The actual search directory for Load and Save can be edited here. Also the default file extension
can be altered.
• Instant View
– Small Window
If you switch on this feature, the small figure at the right of the filelist will show you the
selected signal immediatly after selection.
– Large Window
Every time a new signal is generate (e.g. applying a command to an existing signal) e new
figure window will be opened displaying it.
31
5.3.8
Help
The menu Usage will start your web browser with the HTML-Version of this manual shipped with
the OpenTSTOOL distribution. Run ’help docopt’ at the matlab command prompt to configure
your web brower correctly.
After the seperation line you can view the matlab command line help for every method of the signal
class. The same information is in the HTML- and in the PDF-Version of the manual in class reference
section 6.20.
5.3.9
View
This menu invokes a new figure window viewing the selected signal using the signal/view command
(6.20.3.82). You can also simply type Ctrl-v.
32
Chapter 6
Mex-Function Reference
Parts of TSTOOL’s functionality are coded in mex-files. All TSTOOL mex-files are located in the
directory tstoolbox/mex. It is possible to use these mex-files independently of the full TSTOOL
installation.
6.1
akimaspline - Cubic spline interpolation using Akima
splines
Compared to Matlab’s built-in cubic spline, Akima spline interpolation better copes with discontinuities in a time series.
Syntax:
• yy = akimaspline(x,y,xx)
Input arguments:
• x, y - vectors describing knot data, see Matlab’s original spline function
• xx - vector of positions at which the spline is evaluated
Output arguments:
• yy - evaluated function values
Example:
x = 1:100;
y = floor((x + rand(1, 100))/ pi);
xx = 1:0.1:100;
yy = akimaspline(x, y, xx);
plot(x,y, xx, yy, ’r’)
33
6.2
amutual - compute auto mutual information function
Fast, but crude auto mutual information of a scalar timeseries for the timelags from zero to maxtau.
The input time series should be much longer than maximal timelag maxtau. The algorithm uses
equidistant histogram boxes, so results are bad in a mathematical sense. However, a fast algorithm
based on ternary search trees to store only nonempty boxes is used.
Syntax:
• a = amutual(ts, maxtau, partitions)
Input arguments:
• ts - vector holding time series data
• maxtau - maximal time lag
• partitions - number of partitions for the one-dimensional histogram
Output arguments:
• a - vector of length maxtau+1, holding auto mutual information
6.3
baker - Generate Baker time-series
Generate time-series from the iterated Baker map [150].
Syntax:
• x = baker(length, [eta l1 l2 x0 y0])
Input arguments:
• length - number of samples to generate
• [eta l1 l2 x0 y0] - vector of parameters and initial conditions
Output arguments:
• x - time series
Example:
x = baker(2000, [0.6 0.25 0.4 rand(1,1) rand(1,1)]);
plot(x(1:end-1,2), x(2:end,2), ’.’)
34
6.4
boxcount - Classical boxcounting algorithm
boxcount is a fast algorithm that partitions a data set of points into equally spaced and sized boxes.
The algorithm is based on Robert Sedgewick’s Ternary Search Trees [149] which offer a fast and
efficient way to create and search a multidimensional histogram. Empty boxes require no storage
space, therefore the maximum number of boxes (and memory) used can not exceed the number of
points in the data set, regardless of the data set’s dimension and the number of partitions per axis.
During processing, data values are scaled to be within the range [0,1]. All columns of the input matrix
are scaled by the same factor, so no skewing is introduced into the point set.
Syntax:
• [a,b,c] = boxcount(point set, partitions)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D. D is limited to 128.
• partitions - number of partitions per axis, limited to 16384. For convenience, if a vector is
given, boxcount will iterate over all values of this vector.
Output arguments:
• a - vector of size D with: log2(sum(Number of nonempty boxes))
• b - vector of size D with: sum(p * log2(p)) , where p is the relative frequency of points falling
into a box
• c - vector of size D with: log2(sum(p*p)), where p is the relative frequency of points falling into
a box
Example:
p = rand(50000, 4);
p = p - min(min(p));
p = p ./ max(max(p));
[a,b,c] = boxcount(p, 16)
6.5
cao - Determine minimum embedding dimension by Cao’s
method
This mex-file applies Cao’s method [38] to the input data set. If the data set contains points of
dimension D, it computes E and E* for a data set of dimension 1 (taken from the first column of
the input data set), then for a data set of dimension 2 (taken from the first two columns) up to a
dimension of D. Optionally, this algorithm extends Cao’s method in a straightforward manner to use
more than one nearest neighbors.
Syntax:
• [E, E*] = cao(pointset, query indices, k)
Input arguments:
35
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• k - number of nearest neighbors to compute. Cao’s method can be extended to use more than
only the first nearest neighbor (k=1).
Output arguments:
• E and E* are vectors of size D. Please refer the Cao’s article [38] for a precise description of their
meaning.
6.6
chaosys - integrate dynamical system given by a set of
ordinary differential equations
chaosys gives the user the possibility to compute time series data for a couple of dynamical systems,
among which are Lorenz, Chua, Roessler etc. This routine is not meant as a replacement for Matlab’s
suite of functions for solving ODEs, but as a fast way to generate some data sets to evaluate the
processing capabilities of TSTOOL. The integration is done by an ODE solver using an Adams Pece
scheme with local extrapolation [151]. It is at least faster than Matlab’s native ODE solver. However,
it is not possible to extend the set of systems without recompiling chaosys.
Syntax:
• x = chaosys(length, stepwidth, initial conditions, mode, parameters)
Input arguments:
• length - number of samples to generate
• stepwidth - integration step size
• initial conditions - vector of initial conditions
• mode:
– 0: Lorenz
– 1: Generalized Chua : Double Scroll
– 2: Generalized Chua : Five Scroll
– 3: Duffing
– 4: Roessler
– 5: Toda Oscillator
– 6: Van der Pol Oscillator
– 7: Pendulum
For an exact definition of the ODE systems, please refer to this header file.
• parameters - vector of systems parameters. The order of the parameters is exactly the same as
in the constructors of the DGL subclasses in the above file.
Output arguments:
36
• x contains the output of the integration, organized as matrix of size samples by dim, where dim
is the number of ODEs that define the system
Example:
x = chaosys(20000, 0.025, [0.1 -0.1 0.02], 0);
plot(x(:,1));
Definitions of the ODEs:
The parameters of the odes are a vector of [a,b,...].
Lorenz:
dy1
= a(y1 − y2 )
dt
dy2
= by1 − y2 − y1 y3
dt
dy3
= y1 y2 + cy3
dt
Generalized Chua:
dy1
= a(y1 − by2 )
dt
dy2
= by1 − y2 + y3
dt
dy3
= −cy2
dt
Duffing:
dy1
= y2
dt
dy2
= −y1 − y13 − by2 + a cos y3
dt
dy3
=c
dt
R¨
ossler:
dy1
= −y2 − y3
dt
dy2
= −y1 + ay2
dt
dy3
= b + y3 (y1 − c)
dt
Toda oscillator:
dy1
= 1 + a sin(bt) − by2 − exp y1
dt
dy2
= y1
dt
van der Pol oscillator:
dy1
= a sin(bt) − c(by22 − 1) − d2 y1
dt
dy2
= y1
dt
37
pendulum:
dy1
= a sin(bt) − cby2 − d sin y1
dt
dy2
= y1
dt
6.7
corrsum - Computation of the correlation sum
The topics correlation sum and correlation dimension estimation can also be found here.
Syntax:
• [c, d] = corrsum(pointset, query indices, range, exclude)
• [c, d] = corrsum(pointset, query indices, range, exclude, bins)
• [c, d] = corrsum(atria, pointset, query indices, range, exclude)
• [c, d] = corrsum(atria, pointset, query indices, range, exclude, bins)
Input arguments:
• atria - output of nn prepare for pointset (optional) (cf. Section 6.13)
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• range - search range, may be given in one of two ways
– If only a single value is given, this value is taken as maximal search radius relative to the
attractor diameter (0 < relative range < 1). The minimal search radius is determined
automatically be searching for the minimal interpoint distance in the data set.
– If a vector of length two is given, the values are interpreted as absolut minimal and maximal
search radius.
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
• bins - number of distance values at which the correlation sum is evaluated, defaults to 32
Output arguments:
• c - vector of correlation sums, length(c) = bins
• d - vector of the corresponding distances at which the correlation sums (stored in c) were
computed. d is exponentially spaced, length(c) = bins
Example:
x = chaosys(25000, 0.025, [0.1 -0.1 0.02], 0); % generate data from Lorenz system
x = x(5001:end,:);
% discard first 5000 samples due to transient
% now compute correlation sum up to five percent of attractor diameter
[c,d] = corrsum(x, randref(1,20000, 1000), 0.05, 0);
loglog(d,c)
% and show the result as log-log plot
38
6.8
corrsum2 - Computation of the correlation sum
This is an extended version of the correlation sum algorithm. It tries to accelerate the computation
of the correlation sum by using a different number of reference points at each length scale. For large
length scales, only a few number of reference points will be used since for this scale, quite a lot of
neighbors will fall within this range (and also the search time will be high). The smaller the length
scale, the more reference points are used. The algorithm tries to keep the number of pairs found
within each range roughly constant at Npairs to ensure a good statistic even for the smallest length
scales. However, the number of reference points actually used may be limited to be within [Nref min
Nref max] to give at least some control to the user. All reference points are chosen randomly from
the data set without reoccurences of the same index.
Syntax:
• [c, d, e, f, g] = corrsum(pointset, Npairs, range, exclude)
• [c, d, e, f, g] = corrsum(pointset, Npairs, range, exclude, bins)
• [c, d, e, f, g] = corrsum(pointset, Npairs, range, exclude, bins, opt flag)
• [c, d, e, f, g] = corrsum(atria, pointset, Npairs, range, exclude)
• [c, d, e, f, g] = corrsum(atria, pointset, Npairs, range, exclude, bins)
• [c, d, e, f, g] = corrsum(atria, pointset, Npairs, range, exclude, bins,
opt flag)
Input arguments:
• atria - output of nn prepare for pointset (optional) (cf. Section 6.13)
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• Npairs - Number of pairs to find within each length scale. The algorithm will adapt the number
of reference points while computing the correlation sum. Reference points are chosen randomly
from the pointset. Optionally, a vector of the form [Npairs Nref min Nref max] may be given.
For no length scale less than Nref min reference points will be used. Additionally, not more than
Nref max reference points will be used at all.
• range - search range, may be given in one of two ways
– If only a single value is given, this value is taken as maximal search radius relative to
attractor diameter (0 < relative range < 1). The minimal search radius is determined
automatically be searching for the minimal interpoint distance in the data set.
– If a vector of length two is given, the values are interpreted as absolut minimal and maximal
search radius.
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. E.g. if the index of the query point is 124 and exclude is
set to 3, points with indices 121 to 127 are omitted from search. exclude = 0 means : exclude
self-matches
• bins - number of distance values at which the correlation sum is evaluated, defaults to 32
• opt flag - optional flag to control the algorithm:
– 0 - Use euclidian distance, be verbose, don’t allow to count a pair of points twice
– 1 - Use maximum distance, be verbose, don’t allow to count a pair of points twice
39
– 2 - Use euclidian distance, be verbose, allow to count a pair of points twice
– 3 - Use maximum distance, be verbose, allow to count a pair of points twice
– 4 - Use euclidian distance, be silent, don’t allow to count a pair of points twice
– 5 - Use maximum distance, be silent, don’t allow to count a pair of points twice
– 6 - Use euclidian distance, be silent, allow to count a pair of points twice
– 7 - Use maximum distance, be silent, allow to count a pair of points twice
If the preprocessing output atria is given, the type of metric used to create this overrides the
settings by opt flag.
Output arguments:
• c - vector of correlation sums, length(c) = bins
• d - vector of the corresponding distances at which the correlation sums (stored in c) where
computed. d is exponentially spaced, length(c) = bins
• e - vector of the number of pairs found within this range, length(e) = bins
• f - vector of the number of total pairs that were tested, length(f) = bins
• g - vector containing the indices of the reference points actually used by the algorithm.
Example:
x = chaosys(25000, 0.025, [0.1 -0.1 0.02], 0);
x = x(5001:end,:);
% discard first 5000 samples due to transient
% now compute correlation sum up to five percent of attractor diameter
[c,d] = corrsum2(x,[1000 100 2000], 0.05, 200);
loglog(d,c)
% and show the result as log-log plot
6.9
fnearneigh - Fast nearest neighbor search
fnearneigh is based on the advanced triangle inequality algorithm ATRIA. However, it does not
support approximate queries. The functionality of fnearneigh is almost the same as that of nn search
(cf. Section 6.14), so fnearneigh might become obsolete in future versions of TSTOOL.
Syntax:
• [index, distance] = fnearneigh(pointset, query points, k)
• [index, distance] = fnearneigh(pointset, query indices, k, exclude)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• query points - a R by D double matrix containing the coordinates of the query points, organized
as R points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• k - number of nearest neighbors to be determined
40
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• index - a matrix of size R by k which contains the indices of the nearest neighbors. Each row of
index contains k indices of the nearest neighbors to the corresponding query point.
• distance - a matrix of size R by k which contains the distances of the nearest neighbors to the
corresponding query points, sorted in increasing order.
6.10
gendimest - Estimate generalized dimension spectrum
The Renyi dimension spectrum of a points set can be estimated using information about the distribution of the interpoint distances. Since we are interested in the scaling behaviour of the Renyi
information for small distances, we don’t need to compute all interpoint distances, the distances to k
nearest neighbors for each reference point are sufficient [150].
Robust estimation is used instead of mean square error fitting.
Syntax:
• [dimensions, moments] = gendimest(dists, gammas, kmin low, kmin high, kmax)
Input arguments:
• dists - a matrix of size R by k which contains distances from reference points to their k nearest
neighbors, sorted in increasing order. This matrix can be obtained by calling nn search (cf.
Section 6.14) or fnearneigh (cf. Section 6.9) on the point set whose dimension spectrum is to be
investigated.
• gammas - vector of the moment orders
• kmin low - first kmin, 1 ≤ kmin low
• kmin high - last kmin, kmin low ≤ kmin high < kmax
• kmax - highest neigbor order up to which, kmax ≤ k
Output arguments:
• dimensions - matrix of size length(gammas) by kmin upper-kmin lower+1, holding the dimension estimates
• moments (optional) - matrix of size k by length(gammas), storing the computed moments of the
neigbor distances
Example:
x = chaosys(25000, 0.025, [0.1 -0.1 0.02], 0); % generate data from Lorenz system
x = x(5001:end,:);
% discard first 5000 samples due to transient
[nn, dist] = fnearneigh(x, randref(1, 20000, 1000), 128, 0);
gammas = -5:0.5:5;
gedims = gendimest(dist, gammas, 8, 8, 128);
plot(1-gammas./gedims’, gedims)
xlabel(’q’);ylabel(’D_q’);title(’Renyi dimension’)
41
6.11
henon - Generate henon time-series
Generate time series by iterating the henon map.
Syntax:
• x = henon(length, [a b xo yo])
Input arguments:
• length - number of samples to generate
• [a b xo yo] - vector of parameters and initial conditions
Output arguments:
• x - vector of size D
Example:
x = henon(500, [-1.4 0.3 0.2 0.12]);
plot(x(:,1), x(:,2), ’.’);
6.12
largelyap - Compute separation of nearby trajectories
largelyap is an algorithm very similar to the Wolf algorithm [90] , it computes the average exponential
growth of the distance of neighboring orbits via the prediction error. The increase of the prediction
error vs the prediction time allows an estimation of the largest lyapunov exponent.
Syntax:
• x = largelyap(pointset, query indices, taumax, k exclude)
• x = largelyap(atria, pointset, query indices, taumax, k exclude)
Input arguments:
• atria - output of nn prepare for pointset (optional) (cf. Section 6.13)
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• taumax - maximal time shift
• k - number of nearest neighbors to compute
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• x - vector of length taumax+1, x(tau) = 1/Nref * sum(log2(dist(reference point + tau, nearest
neighbor + tau)/dist(reference point, nearest neighbor)))
[146]
42
6.13
nn prepare - Do nearest neighbor preprocessing
The intention of this mex-file was to reduce the computational overhead of preprocessing for nearest
neighbor or range searching. With nn prepare it is possible to do the preprocessing for a given point
set only once and save the created tree structure into a Matlab variable. This Matlab variable, usually
called atria, can then be used for repeated neighbor searches on the same point set. Most mex-files
that rely on nearest neighbor or range search offer the possibility to use this variable atria as optional
input argument. However, if the underlying point set is altered in any way, the proprocessing has to
be repeated for the new point set. If the preprocessing output does not belong to the given point set,
wrong results or program termination may occur.
Syntax:
• atria = nn prepare(pointset)
• atria = nn prepare(pointset, metric)
• atria = nn prepare(pointset, metric, clustersize)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• metric - (optional) either ’euclidian’ or ’maximum’ (default is ’euclidian’)
• clustersize - (optional) threshold for clustering algorithm, defaults to 64
Example:
pointset = rand(40000, 3);
atria = nn_prepare(pointset);
[c, d] = corrsum(atria, pointset, 1:17:40000, 0.05, 0);
plot(log(d), log(c))
D = takens_estimator(atria, pointset, 1:17:40000, 0.05, 0)
6.14
nn search
Syntax:
• [index, distance] = nn search(pointset, atria, query points, k)
• [index, distance] = nn search(pointset, atria, query points, k, epsilon)
• [index, distance] = nn search(pointset, atria, query indices, k, exclude)
• [index, distance] = nn search(pointset, atria, query indices, k, exclude,
epsilon)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• atria - output of (cf. Section 6.13) nn prepare for pointset
43
• query points - a R by D double matrix containing the coordinates of the query points, organized
as R points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• k - number of nearest neighbors to be determined
• epsilon - (optional) relative error for approximate nearest neighbors queries, defaults to 0 (=
exact search)
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• index - a matrix of size R by k which contains the indices of the nearest neighbors. Each row of
index contains k indices of the nearest neighbors to the corresponding query point.
• distance - a matrix of size R by k which contains the distances of the nearest neighbors to the
corresponding query points, sorted in increasing order.
6.15
predict
State space based prediction using nearest neighbors. The algorithms computes one or more nearest
neighbors to an initial state vector. The images of the nearest neighbors are used to estimate to image
of the initial state vector. The next iteration uses the previously computed image as new initial state
vector [145].
Syntax:
• x = predict(pointset, length, k, stepsize, mode)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• length - number of iterations (length of prediction)
• k - number of nearest neighbors
• stepsize - prediction stepsize, usually one
• mode - (optional) method to estimate image of initial state vector
– 0 - direct prediction, no weight is applied to neighbors
– 1 - direct prediction, biquadratic weight is applied to neighbors
– 2 - integrated prediction, no weight is applied to neighbors
– 3 - integrated prediction, biquadratic weight is applied to neighbors
Output arguments:
• x - data set as double matrix, size length by D
44
6.16
range search
Syntax:
• [count, neighbors] = range search(pointset, atria, query points, r)
• [count, neighbors] = range search(pointset, atria, query indices, r, exclude)
Input arguments:
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• atria - output of (cf. Section 6.13)nn prepare for pointset
• query points - a R by D double matrix containing the coordinates of the query points, organized
as R points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points
• r - range or search radius (r > 0)
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• count - a vector of length R contains the number of points within distance r to the corresponding
query point
• neighbors - a Matlab cell structure of size R by 2 which contains vectors of indices and vectors
of distances to the neighbors for each given query point. This output argument can not be stored
in a standard Matlab matrix because the number of neighbors within distance r is not the same
for all query points. The vectors if indices and distances for one query point have exactly the
length that is given in count. The values in the distances vectors are not sorted..
6.17
return time
return time may be used to find hidden periodicity in multivariate data, e.g. embedded time series
data. It computes a histogram of return times. For any given reference point, return time calculates
the time span until the time series returns to that location in phase space (by means of nearest
neighbors). A histogram of these time spans is computed. Strong peaks in this histogram might be a
sign of periodicity in the data.
Syntax:
• r = return time(pointset, query indices, k, max time, exclude)
• r = return time(atria, pointset, query indices, k, max time, exclude)
Input arguments:
45
• atria - output of nn prepare for pointset (optional) (cf. Section 6.13)
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• k - number of nearest neighbors to be determined
• max time - integer scalar, gives an upper limit for return times that should be considered.
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For example if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• r - vector of length max time, containing the histogram of return times
6.18
takens estimator
Syntax:
• D = takens estimator(pointset, query indices, relative range, exclude)
• D = takens estimator(atria, pointset, query indices, relative range, exclude)
Input arguments:
• atria - output of nn prepare for pointset (optional) (cf. Section 6.13)
• pointset - a N by D double matrix containing the coordinates of the point set, organized as N
points of dimension D
• query indices - query points are taken out of the pointset, query indices is a vector of length
R which contains the indices of the query points (indices may vary from 1 to N)
• relative range - search radius, relative to attractor diameter (0 < relative range < 1)
• exclude - in case the query points are taken out of the pointset, exclude specifies a range of
indices which are omitted from search. For examples if the index of the query point is 124 and
exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0
means: exclude self-matches
Output arguments:
• D - scalar value, estimation of correlation dimension
46
6.19
tentmap - Generate tentmap time-series
Generate samples of the generalized iterated tentmap.
Syntax:
• x = tentmap(length, [h e s x0])
Input arguments:
• length - number of samples to generate
• [h e s x0] - vector of parameters and initial conditions
Output arguments:
• x - time series
Example:
x = tentmap(500, [0 1 0.97 rand(1,1)]);
plot(x)
plot(x(1:end-1), x(2:end), ’.’)
47
6.20
Class signal
6.20.1
Overview
Class signal is TSTOOL’s main class. Objects of this type model real world signals. A signal does not
only store the pure sample values, it holds much more information like axes, units of sample values
or the axes units, and even more descriptive information like labels, command lines and a processing
history.
The majority of functions in the tstoolbox take a signal as input argument and return a processed
signal as output. This allows for combining or chaining of several processing steps in order to get the
desired output.
6.20.2
Attributes
• xaxes cellarray of at least one object of type achse
• core object of type core (cf. Section 6.22)
• description object of type description (cf. Section 6.21)
6.20.3
Member functions
6.20.3.1
abs
Syntax:
• abs(s)
Take absolut value of all data values of signal s. If sample values are complex, abs(s) returns the
complex modulus (magnitude) of each sample.
6.20.3.2
acf
Syntax:
• acf(s, len)
Input arguments:
• len -length of the fft (optional)
Autocorrelation function for real scalar signals, using fft (of length len). If len is ommited a default
value is calculated. The maximum of the calculated length is 128.
6.20.3.3
acp
Syntax:
• acp(s, tau, past, maxdelay, maxdim, nref)
Input arguments:
49
• tau - proper delay time for s
• past - number of samples to exclude before and after reference index (to avoid correlation effects)
• maxdelay - maximal delay (should be much smaller than the lenght of s) (optional)
• maxdim - maximal dimension to use (optional)
• nref - number of reference points (optional)
Auto crossprediction function for real scalar signals for increasing dimension. The default value for
maxdelay is 25% of the input signal’s length. The default for maxdim is 8 and for nref it is 10% of
the input signal’s length.
6.20.3.4
amutual
Syntax:
• amutual(s, maxtau, bins)
Input arguments:
• maxtau - maximal delay (should be much smaller than the lenght of s) (optional)
• bins - number of bins used for histogram calculation (optional)
Auto mutual information function for real scalar signals, can be used to determine a proper delay
time for time-delay reconstruction. The default value for maxtau is 25% of the input signal’s length.
The default number of bins is 128.
X
P (A, B)
I=
P (A, B) log2
P (A)P (B)
6.20.3.5
amutual2
Syntax:
• amutual2(s, len)
Input arguments:
• len - maximal lag
Auto mutual information (average) function for real scalar signals using 128 equidistant partitions.
6.20.3.6
analyze
Syntax:
• analyze(s, maxdim)
Input arguments:
• maxdim - analyze will not use a dimension higher than this limit
Try to do a automatic analysis procedure of a time series. The time series is embedded using the first
zero of the auto mutual information function for the delay time.
50
6.20.3.7
arch
Syntax:
• [rs, archetypes]=arch(s, na, mode=’normalized’)
Input arguments:
• na - number of generated archetypes
• mode - mode can be one of the following : ’normalized’ , ’mean’, ’raw’ (optional)
Archetypal analysis of column orientated data set:
• each row of data is one ’observation’, e.g. the sample values of all channels in a multichannel
measurement at one point in time
• in mode ’normalized’ each column of data is centered by removing its mean and then normalized
by dividing through its standard deviation before the covariance matrix is calculated
• in mode ’mean’ only the mean of every column of data is removed
• in mode ’raw’ no preprocessing is applied to data
Default value for mode is ’normalized’.
6.20.3.8
boxdim
Syntax:
• rs = boxdim(s, bins)
Input arguments:
• s - data points (row vectors)
• bins - maximal number of partition per axis (optional)
Compute the boxcounting (capacity) dimension of a time-delay reconstructed timeseries s for dimensions from 1 to D, where D is the dimension of the input vectors using boxcounting approach. The
default number of bins is 100.
6.20.3.9
cao
Syntax:
• [E1, E2] = cao(s, maxdim, tau, NNR, Nref)
Input arguments:
• s - scalar input signal
• maxdim - maximal dimension
• tau - delay time
• NNR - number of nearest neighbor to use
• Nref - number of reference points (-1 means: use all points)
Estimate minimum embedding dimension using Cao’s method.
The second output argument, E2, can be used to distinguish between deterministic and random data.
51
6.20.3.10
center
Syntax:
• center(s)
Center signal by removing it’s mean.
6.20.3.11
corrdim
Syntax:
• rs = corrdim(s, bins)
Input arguments:
• s - data points (row vectors)
• bins - maximal number of partition per axis (optional)
Compute the correlation dimension of a time-delay reconstructed timeseries s for dimensions from 1
to D, where D is the dimension of the input vectors using boxcounting approach. The default number
of bins is 100.
6.20.3.12
corrsum
Syntax:
• rs = corrsum(s, n, range, past, bins)
Input arguments:
• n - number of randomly chosen reference points (n == -1 means: use all points)
• range - maximal relative search radius (relative to attractor size) 0..1
• past - number of samples to exclude before and after each reference index
• bins - number of bins (optional)
Compute scaling of correlation sum for time-delay reconstructed timeseries s (Grassberger-Proccacia
Algorithm), using fast nearest neighbor search. Default number of bins is 20.
6.20.3.13
corrsum2
Syntax:
• rs = corrsum2(s, npairs, range, past, bins)
Input arguments:
• npairs - number of pairs per bins
• range - maximal relative search radius (relative to attractor size) 0..1
• past - number of samples to exclude before and after each reference index
• bins - number of bins (optional), defaults to 32
Compute scaling of correlation sum for time-delay reconstructed timeseries s (Grassberger-Proccacia
Algorithm), using fast nearest neighbor search.
52
6.20.3.14
crosscorrdim
Syntax:
• rs = crosscorrdim(s, s2, n, range, past, bins)
Input arguments:
• n - number of randomly chosen reference points (n == -1 means : use all points)
• range - maximal relative search radius (relative to size of data set s2) 0..1
• past - number of samples to exclude before and after each reference index
• bins - number of bins (optional)
Compute scaling of cross-correlation sum for time-delay reconstructed timeseries s against signal s2
(with same dimension as s), using fast nearest neighbor search. Reference points are taken out of
signal s, while neigbors are searched in s2. The default number of bins is 32.
6.20.3.15
cut
Syntax:
• rs = cut(s, dim, start, stop)
Input arguments:
• dim - dimension along which the signal is cutted
• start - position where to start the cut
• stop - position where to stop (optional)
Cut a part of the signal. If stop is ommited only the data at start is cutted.
6.20.3.16
db
Syntax:
• db(s, dbmin)
Compute decibel values of signal relative to a reference value that is determined by the signal’s yunit
values below dbmin are set to dbmin. If dbmin is ommited it is set to -120.
6.20.3.17
delaytime
Syntax:
• tau = delaytime(s, maxdelay, past)
Input arguments:
• maxdelay - maximal delay time
• past - ?
Compute optimal delaytime for a scalar timeseries with method of Parlitz and Wichard.
53
6.20.3.18
diff
Syntax:
• diff(s, nth)
Compute the nth numerical derivative along dimension 1. s has be to sampled equidistantly.
6.20.3.19
dimensions
Syntax:
• [bc,in,co] = dimensions(s, bins)
Input arguments:
• s - data points (row vectors)
• bins - maximal number of partition per axis, default is 100
Output arguments:
• bc - scaling of boxes with partititon sizes (log2 − log2 )
• in - scaling of information with partititon sizes (log2 − log2 )
• co - scaling of correlation with partititon sizes (log2 − log2 )
Compute boxcounting, information and correlation dimension of a time-delay reconstructed timeseries
s for dimensions from 1 to D, where D is the dimension of the input vectors using boxcounting approach.
Scale data to be within 0 and 1. Give a sortiment of (integer) partitionsizes with almost exponential
behaviour.
6.20.3.20
display
6.20.3.21
embed
Syntax:
• emb = embed(s, dim, delay, shift, windowtype)
Input arguments:
• dim - embedding dimension
• delay - time delay (optional)
• shift - shift for two sequent time delay vectors (optional)
• windowtype - type of window (optional)
Output arguments:
• emb - n by dim array, each row contains the coordinates of one point
Embeds signal s with embedding dimension dim and delay delay (in samples). s must be a scalar
time series. The default values for dim and delay are equal to one. The default value for windowtype
is ’Rect’, which is currently the only possible value.
54
6.20.3.22
fft
Syntax:
• f = fft(s)
Output arguments:
• f - n by 2 array, the first column contains the magnitudes, the second one the phases.
Fourier transform of scalar signal s.
6.20.3.23
filterbank
Syntax:
• filterbank(s, depth, filterlen)
Filter scalar signal s into 2depth bands of equal bandwith, using maximally flat filters.
6.20.3.24
firstmax
Syntax:
• [xpos, unit] = firstmax(s)
Give information about first local maximum of scalar signal s.
6.20.3.25
firstmin
Syntax:
• [xpos, unit] = firstmin(s)
Give information about first local minimum of scalar signal s.
6.20.3.26
firstzero
Syntax:
• [xpos, unit] = firstzero(s)
Give information about first zero of scalar signal s, using linear interpolation.
55
6.20.3.27
fracdims
Syntax:
• rs = fracdims(s, kmin, kmax, Nref, gstart, gend, past, steps)
• rs = fracdims(s, kmin, kmax, Nref, gstart, gend, past)
• rs = fracdims(s, kmin, kmax, Nref, gstart, gend)
Input arguments:
• kmin - minimal number of neighbors for each reference point
• kmax - maximal number of neighbors for each reference point
• Nref - number of randomly chosen reference points (n == -1 means : use all points)
• gstart - starting value for moments
• gend - end value for moments
• past - (optional) number of samples to exclude before and after each reference index, default is
0
• steps - (optional) number of moments to calculate, default is 32
Compute fractal dimension spectrum D(q) using moments of neighbor distances for time-delay reconstructed timeseries s.
Do the main job - computing nearest neighbors for reference points.
6.20.3.28
getaxis
Syntax:
• a = getaxis(s, dim)
Get one of the currend xaxes.
6.20.3.29
gmi
Syntax:
• gmi(s, D, eps, NNR, len, Nref)
Input arguments:
• D• eps • NNR • len • Nref Generalized mutual information function for a scalar time series
56
6.20.3.30
histo
Syntax:
• histo(s, partitions)
Histogram function using equidistantly spaced partitions.
6.20.3.31
infodim
Syntax:
• rs = infodim(s, bins)
Input arguments:
• s - data points (row vectors)
• bins - maximal number of partition per axis, default is 100
Compute the information dimension of a time-delay reconstructed timeseries s for dimensions from 1
to D, where D is the dimension of the input vectors. Using boxcounting approach. Scale data to be
within 0 and 1. Give a sortiment of (integer) partitionsizes with almost exponential behaviour.
6.20.3.32
infodim2
Syntax:
• rs = infodim2(s, n, kmax, past)
Input arguments:
• n - number of randomly chosen reference points (n == -1 means : use all points)
• kmax - maximal number of neighbors for each reference point
• past - number of samples to exclude before and after each reference index
Compute scaling of moments of the nearest neighbor distances for time-delay reconstructed timeseries
s. This can be used to calculate information dimension D1.
Numerically compute first derivative of log γ(k) after k.
6.20.3.33
int
Syntax:
• int(s)
Numerical integration along dimension 1 signal s has to be sampled equidistantly.
57
6.20.3.34
intspikeint
Syntax:
• rs = intspikeint(s)
Compute the interspike intervalls for a spiked scalar timeseries, using transformation on ranked values.
6.20.3.35
intspikint
Syntax:
• rs = intspikeint(s)
Compute the interspike intervalls for a spiked scalar timeseries, using transformation on ranked values.
6.20.3.36
largelyap
Syntax:
• rs = largelyap(s, n, stepsahead, past, nnr)
Input arguments:
• n - number of randomly chosen reference points (-1 means: use all points)
• stepsahead - maximal length of prediction in samples
• past - exclude
• nnr - number of nearest neighbours (optional)
Output arguments:
• rs Compute the largest lyapunov exponent of a time-delay reconstructed timeseries s, using formula (1.5.
of Nonlinear Time-Series Analysis, Ulrich Parlitz 1998 [146]).
6.20.3.37
level adaption
Syntax:
• level adaption(s, timeconstants, dynamic limit, threshold)
Each channel of signal s is independently divided by a scaling factor that adapts to the current level
of the samples in this channel. The adaption process is simulated using a cascade of feedback loops
(P¨
uschel 1998) which consists of low pass filters with time constants given as second argument to this
function. The number of time constants given determines the number of feedback loops that are used.
Higher values for time constants will result in slower adaption speed. Short time changes in the signal
will be transmitted almost linearily. In each feedback loop, a nonlinear compressing characteristic
(see Stefan M¨
unkner 1993) limits the signal values to be within [-dynamic limit dynamic limit].
A low value for dynamic limit will introduce nonlinear distortions to the signal.
To prevent the feedback loops from adapting to a zero level (in case all input values are zero), a tiny
threshold is given as 4th argument. The scaling factors will not shrink below this threshold.
58
6.20.3.38
localdensity
Syntax:
• rs = localdensity(s, n, past)
Input arguments:
• n - number of nearest neighbour to compute
• past - a nearest neighbour is only valid if it is as least past timesteps away from the reference
point past = 1 means: use all points but ref point itself
Uses accelerated searching, distances are calculated with euclidian norm.
6.20.3.39
max
Syntax:
• [maximum, yunit, xpos, xunit] = max(s)
Give information about maximum of scalar signal s.
Example:
disp(’maximum of signal : ’)
disp([’y = ’ num2str(m) ’ ’ label(yunit(s))]);
disp([’x = ’ num2str(xpos) ’ ’ label(a)]);
6.20.3.40
medianfilt
Syntax:
• rs = medianfilt(s, len)
Moving median filter of width len samples for a scalar time series (len should be odd).
6.20.3.41
merge
Syntax:
• merge(signal1, signal2, dB)
• merge(signal1, signal2)
Input arguments:
• signal1, signal2 - Signals
• dB - energy ratio, (optional, default = 0)
Merges signal s1 and s2 into a new signal with energy ration dB (in decibel) a positive value of dB
increases the amount of signal1 in the resulting signal.
59
6.20.3.42
min
Syntax:
• [minimum, yunit, xpos, xunit] = min(s)
Give information about minimum of scalar signal s.
Example:
disp(’minimum of signal : ’)
disp([’y = ’ num2str(m) ’ ’ label(yunit(s))]);
disp([’x = ’ num2str(xpos) ’ ’ label(a)]);
6.20.3.43
minus
Syntax:
• rs=minus(s, offset)
• rs=minus(s1,s2)
Input arguments:
• s, s1, s2 - signal object
• offset - scalar value
Calculate difference of signals s1 and s2 or substract a scalar value from s.
6.20.3.44
movav
Syntax:
• rs = movav(s, len, windowtype)
• rs = movav(s, len)
Moving average of width len (samples) along first dimension.
6.20.3.45
multires
Syntax:
• rs = multires(s) => scale=3
• rs = multires(s, scale)
Multires perform multiresolution analysis. Y = MULTIRES (X,H,RH,G,RG,SC) obtains the SC successive details and the low frequency approximation of signal in X from a multiresolution scheme. The
analysis lowpass filter H, synthesis lowpass filter RH, analysis highpass filter G and synthesis highpass
filter RG are used to implement the scheme.
Results are given in a scale+1 channels. The first scale channels are the details corresponding to the
scales 21 to 2scale the last row contains the approximation at scale 2SC . The original signal can be
restored by summing all the channels of the resulting signal.
60
6.20.3.46
nearneigh
Syntax:
• rs = nearneigh(s, n) => past=1
• rs = nearneigh(s, n, past)
Input arguments:
• n - number of nearest neighbour to compute
• past - a nearest neighbour is only valid if it is as least past timesteps away from the reference
point. past = 1 means: use all points but ref point itself
n nearest neighbour algorithm. Find n nearest neighbours (in order of increasing distances) to each
point in signal s uses accelerated searching, distances are calculated with euclidian norm.
6.20.3.47
norm1
Syntax:
• rs=norm1(s) => low=0 , upp=1
• rs=norm1(s, low) => upp=1
• rs=norm1(s, low, upp)
Scale and move signal values to be within [low,upp].
6.20.3.48
norm2
Syntax:
• rs=norm2(s)
Normalize signal by removing it’s mean and dividing by the standard deviation.
6.20.3.49
pca
Syntax:
• [rs, eigvals, eigvecs] = pca(s) => mode=’normalized’ , maxpercent = 95
• [rs, eigvals, eigvecs] = pca(s, mode) => maxpercent = 95
• [rs, eigvals, eigvecs] = pca(s, mode, maxpercent)
Input arguments:
• each row of data is one ’observation’, e.g. the sample values of all channels in a multichannel
measurement at one point in time
• mode can be one of the following : ’normalized’ (default), ’mean’, ’raw’
61
– in mode ’normalized’ each column of data is centered by removing its mean and then
normalized by dividing through its standard deviation before the covariance matrix is calculated
– in mode ’mean’ only the mean of every column of data is removed
– in mode ’raw’ no preprocessing is applied to data
• maxpercent gives the limit of the accumulated percentage of the resulting eigenvalues, default
is 95 %
Principal component analysis of column orientated data set.
6.20.3.50
plosivity
Syntax:
• rs = plosivity(s, blen) => flen=1 , thresh=0, windowtype = ’Rect’
• rs = plosivity(s, blen, flen) => thresh=0, windowtype = ’Rect’
• rs = plosivity(s, blen, flen, thresh) => windowtype = ’Rect’
• rs = plosivity(s, blen, flen, thresh, windowtype)
Compute plosivity of a spectrogram. See also: window for list of possible window types.
6.20.3.51
plus
Syntax:
• rs=plus(s, offset)
• rs=plus(s1, s2)
Add two signals s1 and s2 or add a scalar value offset to s.
6.20.3.52
poincare
Syntax:
• rs=poincare(s, ref)
Compute Poincare-section of an embedded time series the result is a set of vector points with dimension
DIM-1, when the input data set of vectors had dimension DIM. The projection is done orthogonal to
the tangential vector at the vector with index.
6.20.3.53
power
Syntax:
• power(s)
Calculate squared magnitude of each sample.
62
6.20.3.54
predict
Syntax:
• rs = predict(s, dim, delay, len) => nnr=1
• rs = predict(s, dim, delay, len, nnr) => mode=0
• rs = predict(s, dim, delay, len, nnr, mode)
Input arguments:
• dim - dimension for time-delay reconstruction
• delay - delay time (in samples) for time-delay reconstruction
• len - length of prediction (number of output values)
• nnr - number of nearest neighbors to use (default is one)
• step - stepsize (in samples) (default is one)
• mode:
– 0 = Output vectors are the mean of the images of the nearest neighbors
– 1 = Output vectors are the distance weighted mean of the images of the nearest neighbors
– 2 = Output vectors are calculated based on the local flow using the mean of the images of
the neighbors
– 3 = Output vectors are calculated based on the local flow using the weighted mean of the
images of the neighbors
Local constant iterative prediction for scalar data, using fast nearest neighbor search. Four methods
of computing the prediction output are possible.
6.20.3.55
predict2
Syntax:
• rs = predict2(s, len, nnr, step, mode)
Input arguments:
• len - length of prediction (number of output values)
• nnr - number of nearest neighbors to use (default is one)
• step - stepsize (in samples) (default is one)
• mode:
– 0 = Output vectors are the mean of the images of the nearest neighbors
– 1 = Output vectors are the distance weighted mean of the images of the nearest neighbors
– 2 = Output vectors are calculated based on the local flow using the mean of the images of
the neighbors
– 3 = Output vectors are calculated based on the local flow using the weighted mean of the
images of the neighbors
Local constant iterative prediction for phase space data (e.g. data stemming from a time delay
reconstruction of a scalar time series), using fast nearest neighbor search. Four methods of computing
the prediction output are possible.
63
6.20.3.56
rang
Syntax:
• rs = rang(s)
Transform scalar time series to rang values.
6.20.3.57
removeaxis
Syntax:
• s = removeaxis(s, dim)
Remove axis one of the current xaxes. No bound checking for dim.
6.20.3.58
return time
Syntax:
• rs = return time(s, nnr, maxT) => past=1
• rs = return time(s, nnr, maxT, past)
• rs = return time(s, nnr, maxT, past, N)
Input arguments:
• nnr - number of nearest neighbors
• maxT - maximal return time to consider
• past - a nearest neighbor is only valid if it is as least past timesteps away from the reference
point past = 1 means: use all points but tt ref point itself
• N - number of reference indices
Compute histogram of return times.
6.20.3.59
reverse
Syntax:
• rs=reverse(s)
Reverse signal along dimension 1.
6.20.3.60
rms
Syntax:
• rs = rms(s)
Calculate root mean square value for signal along dimension 1.
64
6.20.3.61
scale
Syntax:
• scale(signal, factor)
Scale signal by factor f.
6.20.3.62
scalogram
Syntax:
• rs = scalogram(s) => scalemin=0.1
• rs = scalogram(s, scalemin) => scalemax=1
• rs = scalogram(s, scalemin, scalemax) => scalestep=0.1
• rs = scalogram(s, scalemin, scalemax, scalestep) => mlen=10
• rs = scalogram(s, scalemin, scalemax, scalestep, mlen)
Scalogram of signal s using morlet wavelet. See also: spec2.
6.20.3.63
setaxis
Syntax:
• s = setaxis(s, dim, achse)
Change one of the current xaxes.
6.20.3.64
setunit
Syntax:
• s = setunir(s, dim, u)
Change unit of one of the current xaxes.
6.20.3.65
shift
Syntax:
• s = shift(s, distance) (dim=1)
• s = shift(s, distance, dim)
shift signal on axis No. dim by distance (measured in the unit of the axis) to the right
65
6.20.3.66
signal
Syntax:
• s = signal(array)
creates a new signal object from a data array array the data inside the object can be retrieved
with x = data(s);
• s = signal(array, achse1, achse2, ...)
creates a new signal object from a data array array, using achse1 etc. as xachse entries
• s = signal(array, unit1, unit2, ...)
creates a new signal object from a data array ’array’, using unit1 etc. to create xachse objects
• s = signal(array, samplerate1, samplerate2, ...)
creates a new signal object from a data array array, using as xunit ’s’ (second) and scalar
samplerate1 as samplerate(s)
A signal object contains signal data, that is a collection of real or complex valued samples. A signal
can be one or multi-dimensional. The number of dimensions is the number of axes that are needed to
describe the the data.
An example for an one-dimensional signal is a one-channel measurement (timeseries), or the power
spectrum of a one-channel measurement. An example for a two-dimensional signal is a twelve-channel
measurement, with one time axis and a ’channel’ axis. Another example for a two-dimensional signal
is a short time spectrogramm of a time series, where we have a time axis and a frequency axis.
Each axis can have a physical unit(e.g. ’s’ or ’Hz’), a starting point and a step value. E.g. if a
time-series is sampled with 1000 Hz, beginning at 1 min 12 sec, the unit is ’s’, the starting point is 72
and the step value (delta) is 0.001.
But not only the axes have physical units, also the sample value themselve can have a unit, maybe
’V’ or ’Pa’, depending on what the sampled data represent (=¿ yunit)
All units are stored as objects of class ’unit’, all axes are stored as objects of class ’achse’ (this
somewhat peculiar name was chosen because of conflicts with reserved matlab keywords ’axis’ and
’axes’, which otherwise would have been the first choice).
Example for creating a 2-dimensional signal with y-unit set to ’Volt’, the first dimension’s unit is
’second’ (time), the second dimension’s unit is ’n’ (Channels).
Examples:
•
tmp = rand(100, 10);
s = signal(tmp, unit(’s’), unit(’n’));
s = setyunit(s, unit(’V’));
s = addcomment(s, ’Example signal with two dimensions’)
• Loading from disk
s = signal(filename)
loads a previously stored signal object
• Importing from other file formats:
ASCII: s = signal(’data/spalte1.dat’, ’ASCII’)
WAVE: s = signal(’data/Sounds/hat.wav’, ’WAVE’)
AU (SUN AUDIO): s = signal(’data/Sounds/hat.au’, ’AU’)
(old) NLD-Format : s = signal(’test.nld’, ’NLD’)
66
6.20.3.67
spacing
• v = spacing(s) (dim=1)
• v = spacing(s, dim)
return spacing values for xaxis nr. dim
6.20.3.68
spec
Syntax:
• rs = spec(s)
compute power spectrum for real valued scalar signals. Multivariate signals are accepted but may
produce unwanted results as only the spectrum of the first column is returned.
6.20.3.69
spec2
Syntax:
• rs = spec2(s)
Input Arguments:
• fensterlen - size of window (optional)
• fenster - window type (optional)
• vorschub - shift in samples (optional)
spectrogramm of signal s using short time fft
Examples:
view(spec2(sine(10000, 1000, 8000), 512, ’Hanning’))
6.20.3.70
stts
Syntax:
• rs = stts(s, I) (J=0, K=1, L=1)
• rs = stts(s, I, J) (K=1, L=1)
• rs = stts(s, I, J, K) (L=1)
• rs = stts(s, I, J, K, L)
Input Arguments:
• s - input data set of N snapshots of length M, given as N by M matrix
• I - number of spatial neighbours
• J - number of temporal neighbours (in the past)
• K - spatial shift (= spatial delay)
• L - temporal delay
Spatiotemporal prediction conforming to U. Parlitz, NONLINEAR TIME-SERIES ANALYSIS Chapter 1.10.2.1.
67
6.20.3.71
sttserror
Syntax:
• rs = sttserror(s1, s2)
Input Arguments:
• s1 - original signal
• s2 - predicted signal
compute error function for prediction of spatial-temporal systems
see U. Parlitz "Nonlinear Time Series Analysis", Section 1.10.2.2 Eq. 1.10
6.20.3.72
surrogate1
Syntax:
• rs = surrogate1(s)
create surrogate data for a scalar time series by randomizing phases of fourier spectrum
see : James Theiler et al.’Using Surrogate Data to Detect Nonlinearity in Time Series’, APPENDIX
: ALGORITHM I
6.20.3.73
surrogate2
Syntax:
• rs = surrogate2(s)
create surrogate data for a scalar time series
see : James Theiler et al.’Using Surrogate Data to Detect Nonlinearity in Time Series’, APPENDIX
: ALGORITHM II
6.20.3.74
surrogate3
Syntax:
• rs = surrogate3(s)
create surrogate data for a scalar time series by permuting samples randomly
6.20.3.75
surrogate test
Syntax:
• rs=surrogate test(s, ntests, method,func)
Input Arguments:
• s - has to be a real, scalar signal
68
• ntests - is the number of surrogate data sets to create
• method - method to generate surrogate data sets:
– 1: surrogate1
– 2: surrogate2
– 3: surrogate3
• func - string with matlab-code, have to return a signal object with a scalar time series. The
data to process is a signal object referred by the qualifier s (see example).
Output Arguments:
• rs is a signal object with a three dimensional time series. The first component is the result of
the func function applied to the original data set s. The second component is the mean of the
result of the func function applied to the ntests surrogate data sets. The third component is
the standard deviation. There is a special plothint (’surrerrorbar’) for the view function to
show this result in the common way.
surrogate test runs an automatic surrogate data test task. It generates ntests surrogate data sets
an performs the func function to each set. func is a string with matlab-code who returns a signal s
with a scalar time series.
Example:
st = surrogate_test(s, 10, 1, 1, ’largelyap(embed(s,3,1,1), 128,20,10);’);
6.20.3.76
swap
Syntax:
• rs = swap(s) (exchange dimension 1 and dimension 2)
• rs = swap(s, dim1, dim2)
Exchange signal’s dimensions (and axes)
6.20.3.77
takens estimator
Syntax:
• D2 = takens estimator2(s, n, range, past)
Input Arguments:
• n - number of randomly chosen reference points (n == -1 means : use all points)
• range - maximal relative search radius (relative to attractor size) 0..1
• past - number of samples to exclude before and after each reference index
Takens estimator for correlation dimension
69
6.20.3.78
tc3
Syntax:
• rs = tc3(s,tau,n,method)
Input Arguments:
• tau - see explaination below
• n - number of surrogate data sets to generate
• method - method to generate the surrogate data sets:
– 1: surrogate1
– 2: surrogate2
– 3: surrogate3
Output Arguments:
• rs is a row vector, returned as signal object. The first item is the TC3 value for the original
data set s. The following n values are the TC3 values for the generated surrogates. There exist
a special plothint (’surrbar’) for the view function to show this kind of result in the common
way.
This function calculates a special value for the original data set and the n generated surrogate data
sets. The TC3 value is defined as followed:
TC3 ({xn }, τ ) =
hxn xn−τ xn−2τ i
3
|hxn xn−τ i| 2
In terms of surrogate data test this is a test statistics for higher order moments. The original tc3
function is located under utils/tc3.m and use simple matlab vectors.
6.20.3.79
trend
Syntax:
• rs = trend(s, len)
trend correction
calculate moving average of width len (samples) for a scalar time series (len should be odd) and
remove the result from the input signal
6.20.3.80
trev
Syntax:
• rs = trev(s,tau,n,method)
Input Arguments:
• tau - see explaination below
• n - number of surrogate data sets to generate
70
• method - method to generate the surrogate data sets:
– 1: surrogate1
– 2: surrogate2
– 3: surrogate3
Output Arguments:
• rs is a row vector, returned as signal object. The first item is the TREV value for the original
data set s. The following n values are the TREV values for the generated surrogates. There exist
a special plothint (’surrbar’) for the view function to show this kind of result in the common
way.
This function calculates a special value for the original data set and the n generated surrogate data
sets. The TREV value is defined as followed:
TREV ({xn }, τ ) =
h(xn − xn−τ )3 i
3
h(xn − xn−τ )2 i 2
In terms of surrogate data test this is a test statistics for time reversibility. The original trev function
is located under utils/trev.m and use simple matlab vectors.
6.20.3.81
upsample
Syntax:
• rs = upsample(s, factor, method)
Input Arguments:
• method may be one of the following :
– ’fft’
– ’spline’
– ’akima’
– ’nearest’
– ’linear’
– ’cubic’
• s has be to sampled equidistantly for fft interpolation
Change sample rate of signal s by one-dimensional interpolation
6.20.3.82
view
Syntax:
• view(signal) (fontsize=12)
• view(signal, fontsize)
• view(signal, fontsize, figurehandle)
71
Signal viewer that decides from the signal’s attributes which kind of plot to produce, using the signal’s
plothint entry to get a hint which kind of plot to produce
Possible plothints are:
• ’graph’
• ’bar’
• ’surrbar’
• ’surrerrorbar’
• ’points’
• ’xyplot’
• ’xypoints’
• ’scatter’
• ’3dcurve’
• ’3dpoints’
• ’spectrogram’
• ’image’
• ’multigraph’
• ’multipoints’
• ’subplotgraph’
6.20.3.83
write
Syntax:
• write(s, filename) (writes in TSTOOL’s own file format)
• write(s, filename, ’ASCII’)
• write(s, filename, ’WAV’) (RIFF WAVE FORMAT)
• write(s, filename, ’AU’) (SUN AUDIO FORMAT)
• write(s, filename, ’NLD’) (old NLD FORMAT)
• write(s, filename, ’SIPP’) (si++ file format)
writes a signal object to file filename (uses matlab’s file format)
6.21
Class description
6.21.1
Overview
Class description is the second base class of class signal (cf. Section 6.20). An object of type description
stores all descriptive information belonging to a signal.
72
6.21.2
Attributes
• label - string
• name - string
• type - string
• plothint - string
• comment - object of type list (cf. Section 6.25)
• history - object of type list (cf. Section 6.25)
• creator - string
• yname - string
• yunit - object of type unit (cf. Section 6.24)
• commandlines - object of type list (cf. Section 6.25)
• optparam - cell array, may be used to store optional information
6.21.3
Member functions
6.21.3.1
addcommandlines
adds new commandline to list of commands that have been applied to that signal
example 1 addcommandlines(s, ’s = spec2(s’, 512, ’Hanning’ )) will add ’s = spec2(s,
512, ’Hanning’);’ to the list of applied commands
example 2 len = 512; text = ’Hanning’; addcommandlines(s, ’s = spec2(s’, 512,
’Hanning’ )) will add ’s = spec2(s, 512, ’Hanning’);’ to the list of applied commands
6.21.3.2
addcomment
adds new comment to current list of comments
6.21.3.3
addhistory
adds text to current history list always the current time and date is written into the first line
6.21.3.4
commandlines
6.21.3.5
comment
6.21.3.6
creator
6.21.3.7
description
description class constructor Syntax:
• d = description()
• d = description(name)
73
• d = description(name, type)
• d = description(yunit)
An object of class description contains auxiliary descriptive information for a signal, e.g. information
about data unit, creator, how the signal should be plotted, a user specified comment text, a processing
history and the commandlines that were used to generate this signal
6.21.3.8
display
description/display
6.21.3.9
history
description/history
6.21.3.10
label
6.21.3.11
makescript
Syntax:
• makescript (signal, scriptfilename)
creates a Matlab m-file that contains exactly the the processing steps that have been applied to get
the input signal. This gives a kind of macro facility for tstool.
Example signal s was calculated through several processing steps from signal s0 (the raw or original
signal) Now makescript(s, ’foo.m’) will create a Matlab m-file named foo.m which, applied
to s0, will give s.
6.21.3.12
merge
Syntax:
• d = merge(d1, d2)
merge two descriptions
Most items are taken from first description. History is taken from both descriptions. This function
may be useful when writing binary operators for class signal
6.21.3.13
name
description/name Syntax:
• n = name(d)
Get signal’s name
74
6.21.3.14
newcomment
Syntax:
• d = newcomment(d, string)
• d = newcomment(d, list)
Replace old comment with new comment
6.21.3.15
optparams
Syntax:
• param = optparams(d, nr)
get optional parameter number nr
6.21.3.16
plothint
6.21.3.17
setlabel
Syntax:
• d = setlabel(d, label)
the label field of a description is used to give a signal some ’tag’ which remains constant through
various processing steps
e.g. which topic this signal belongs to
6.21.3.18
setname
Syntax:
• d = setname(d, name)
the name field of a descriptiom is used when the signal is loaded from file, it will not be continued
through several processing steps
6.21.3.19
setoptparams
Syntax:
• d = setoptparams(d, nr, param)
set optional parameter number nr
6.21.3.20
setplothint
6.21.3.21
settype
Syntax:
• d = settype(d, string)
Set a new type for signal
75
6.21.3.22
setyname
Syntax:
• d = setyunit(d, string)
Set signal’s y-name
e.g. d = setyunit(d, ’V’)
6.21.3.23
setyunit
Syntax:
• d = setyunit(d, unit)
• d = setyunit(d, string)
Set signal’s y-unit
e.g. d = setyunit(d, ’V’)
6.21.3.24
type
return signal type (e.g. ’Correlation function’, ’Spectrogram’ etc.)
6.21.3.25
yname
return name of the measured data (e.g. ’Heartbeat rate’, ’Current’ etc.)
6.21.3.26
yunit
return y-unit of the sampled data values (e.g. Volt, Pa etc.)
6.22
Class core
6.22.1
Overview
Class core is a base class of class signal (cf. Section 6.20). An object of type core stores the pure sample
values of a signal, without any additional descriptive information. The separation of the numerical
and the descriptive part of a signal simplifies the writing of m-files that work on signals.
6.22.2
Attributes
• data - double matrix (one, two or multidimensional)
TSTOOL stores a one-dimensional time-series always as a row vector ! Rows correspond to the
first xaxis, columns to the second ...
• dlens - double vector, storing size of data
76
6.22.3
Member functions
6.22.3.1
acf
Syntax:
• acf(cin, m)
Input Arguments:
• cin core object
• m fft-length
acf calculates the autocorrelation function of cin via fft of length m.
6.22.3.2
amutual2
Syntax:
• amutual(cin, len)
Input Arguments:
• cin core object
• len maximal lag
amutual2 calculates the mutual information of a time series against itself, with increasing lag uses
equidistant partitioning to compute histograms.
6.22.3.3
compare
Syntax:
• compare(c1,c2, tolerance)
Input Arguments:
• c1,c2 core object of two signals
• tolerance tolerance of the signals’s RMS value (default tolerance=1e-6)
compare compare two signals whether they have equal values slight differences due to rounding errors
are ignored depending on the value of tolerance when signals are found to be not equal, a zero is
returned.
6.22.3.4
core
core class constructor Syntax:
• c = core(arg)
Input Arguments:
• arg double array
A core object contains the pure data part of a signal object.
Methods: ndim dlens data
77
6.22.3.5
data
Syntax:
• d = data(c, varargin)
• c=core object
Input Arguments:
• varargin - selector string for data-elements in matlab notation
Return signal’s data values
With no extra arguments, data returns the data array of a signal object
Another possible call is : data(signal, ’:,:,1:20’)
6.22.3.6
db
Syntax:
• cout = db(cin, ref, scf, dbmin)
Input Arguments:
• cin - core object
• ref - reference value
• scf - scaling factor
• dbmin - minimal db-value
compute decibel values to reference value ref and scaling factor (10 or 20) scf
6.22.3.7
diff
Syntax:
• cout = diff(cin, nth, delta)
Input Arguments:
• cin - core object
• nth - number of derivations
• delta - time difference between to signal values
nth numerical derivative along dimension 1 when data was sampled equidistantly with samplerate =
1/delta
78
6.22.3.8
display
Syntax:
• display(c)
Input Arguments:
• c - core object
6.22.3.9
dlens
Syntax:
• d=dlens(c, nr)
Input Arguments:
• c - core object
returns sizes of dimensions (same as function ’size’ under matlab)
6.22.3.10
embed
Syntax:
• cout = embed(cin, dim, delay, shift, windowtype)
Input Arguments:
• cin - core object
• dim - embed dimension
• delay - delay time in samples for time delay vectors
• shift - shift in samples for two sequent time delay vectors
• windowtype - type of window
Create time delay vectors with dimension dim, delay is measured in samples
The input must be a scalar time series
The result is a n by dim array, each row contains the coordinates of one point
6.22.3.11
filterbank
Syntax:
• filterbank(cin,H,G,ORDER,BASIS)
Input Arguments:
• H - lowpass filter
79
• G - highpass filter
• ORDER - indicates the type of tree:
– 0 - band sorting according to the filter bank
– 1 - band sorting according to the frequency decomposition
• BASIS - desired subband decomposition
calculates the Wavelet Packet Transform of cin. It can be obtained using a selection algorithm function.
It may be switched from one format to another using CHFORMAT. The different bands are sorted
according to ORDER and BASIS. If BASIS is omitted, the output is a matrix with the coefficients
obtained from all the wavelet packet basis in the library. Each column in the matrix represents the
outputs for a level in the tree. The first column is the original signal. If the length of X is not a power
of 2, the columns are zero padded to fit the different lengths. Run the script ’BASIS’ for help on the
basis format.
See also: IWPK, CHFORMAT, PRUNEADD, PRUNENON, GROWADD, GROWNON.
6.22.3.12
int
Syntax:
• cout = int(cin, delta)
Input Arguments:
• cin - core object
• delta - time period between two data samples
numerical integration along dimension 1 when data was sampled equidistantly with samplerate =
1/delta
6.22.3.13
intermutual
Syntax:
• intermutual(cin1,cin2,n)
Input Arguments:
• cin1,cin2 - core objects
Calculates the mutual information of cin1 and cin2.
6.22.3.14
isempty
Syntax:
• r = isempty(s)
Input Arguments:
• s - core object
test if core contains no (valid) data
80
6.22.3.15
medianfilt
Syntax:
• medianfilt(cin,len)
Input Arguments:
• cin - core object
moving median filter
6.22.3.16
minus
Syntax:
• minus(c1,c2)
Input Arguments:
• c1,c2 - core objects
subtract c2 from each columns of c1
6.22.3.17
movav
Syntax:
• movav(cin,len)
Input Arguments:
• cin - core object
• len - average length
moving average
6.22.3.18
multires
Syntax:
• multires(cin,h,rh,g,rg,sc)
Input Arguments:
• cin - core object
81
6.22.3.19
ndim
Syntax:
• ndim(c)
Input Arguments:
• c - core object
return number of dimensions, a scalar value has 0 dimensions
6.22.3.20
norm1
Syntax:
• cout = norm1(cin,low,upp)
Input Arguments:
• cin - core object
• low - column number
• upp - column number
normalize each single column of a the core object to be within [low,upp]
6.22.3.21
norm2
Syntax:
• cout = norm2(cin)
Input Arguments:
• cin - core object
normalize signal by removing it’s mean and dividing by the standard deviation
6.22.3.22
plus
Syntax:
• plus(c1,c2)
Input Arguments:
• c1,c2 - core objects
add c2 to each columns of c1
82
6.22.3.23
rang
Syntax:
• cout = rang(cin)
Input Arguments:
• cin - core object
6.22.3.24
rms
Syntax:
• cout = rms(cin)
Input Arguments:
• cin - core object
compute root mean square value of each column of c1
6.22.3.25
scalogram
Syntax:
• cout = scalogram(cin, smin, smax, sstep, tim)
6.22.3.26
spec
Syntax:
• cout = spec(cin)
Input Arguments:
• cin - core object
compute power spectrum for real valued signals
6.22.3.27
spec2
Syntax:
• cout = spec2(cin, fensterlen, fenster, vorschub)
Input Arguments:
• cin - core object
• fensterlen - window size
• fenster - type of window
• vorschub - moving step
spectrogramm of data using short time fft
83
6.22.3.28
surrogate1
Syntax:
• cout = surrogate1(cin)
Input Arguments:
• cin - core object
create surrogate data for a scalar time series by randomizing phases of fourier spectrum
see : James Theiler et al.’Using Surrogate Data to Detect Nonlinearity in Time Series’, APPENDIX
: ALGORITHM I
6.22.3.29
surrogate2
Syntax:
• cout = surrogate2(cin)
Input Arguments:
• cin - core object
create surrogate data for a scalar time series
see : James Theiler et al.’Using Surrogate Data to Detect Nonlinearity in Time Series’, APPENDIX
: ALGORITHM II
6.22.3.30
surrogate3
Syntax:
• cout = surrogate3(cin)
Input Arguments:
• cin - core object
create surrogate data for a scalar time series by permuting samples randomly
6.22.3.31
uminus
Syntax:
• r = uminus(c)
Input Arguments:
• c - core object
negate time series
84
6.22.3.32
vertcat
Syntax:
• r = vertcat(c1,c2)
Input Arguments:
• c1,c2 - core objects
catenate two timeseries verticaly
6.23
Class achse
6.23.1
Overview
Class achse models an axis, e.g. a time axis or a frequency axis. A signal has a least one axis (if it
is a one dimensional signal). A multidimensional signal has several achse objects. An achse object
is basically described by an object of class unit and the spacing values. The spacing may be linear,
logarithmic or arbitrary (in case of non-uniform sampling).
6.23.1.1
Why is class achse not called class axis ?
The names axis and axes are already occupied in Matlab. So, achse, which is the german translation
of axis, was used as name for that class.
6.23.2
Attributes
• name - string, name of axis (e.g. ’Time’)
• quantity - string
• unit - object of type unit (cf. Section 6.24)
• resolution - string, may be ’linear’, ’logarithmic’ or ’arbitrary’
• first - double value, starting value of this axis
• delta - double value, stepwidth for this axis
• values - double vector, stores spacing values in case of ’arbitrary’ resolution
• opt - cell array, may be used to store optional information
6.23.3
Member functions
6.23.3.1
achse
achse class constructor
Syntax:
• a = achse
creates default achse object
85
• a = achse(axs)
copies achse object axs into a
• a = achse(unt)
creates achse object using unit unt, with linear spacing, first = 0, delta = 1
• a = achse(vec)
creates achse object with arbitrary spacing, using values in vec as spacing data
• a = achse(unt, vec)
creates achse object using unit unt with arbitrary spacing, using values in vec as spacing data
• a = achse(unt, first, delta)
creates achse object with linear spacing, using delta and first
• a = achse(unt, first, delta, ’log’)
creates achse object with logarithmic spacing, using delta and first
achse used to describe the different dimensions (axes) of a signal object.
Example:
• a = achse(unit(’Hz’), 0.01, 10, ’log’)
creates a logarithmic frequency axis with values 0.01 Hz, 0.1 Hz, 1 Hz, 10 Hz
• a = achse(label, samplerate)
has the same result as
a = achse(unit(label), 0, 1/samplerate)
see also: delta first horzcat label name quantity resolution samplerate scale setname spacing unit
6.23.3.2
cut
Syntax:
• a = cut(a, start, stop)
Cut a part out of achse a, beginning from index start up to index stop. stop is only needed in case
of arbitrary spacing. cut ensures the following:
If values = spacing(achse1, N) and N > n then
values(n:N) == spacing(cut(achse1, n), N+1-n)
See also: horzcat
6.23.3.3
delta
6.23.3.4
display
6.23.3.5
eq
Test if achse a and achse b are equal.first is not (!) taken into account for this test.
86
6.23.3.6
first
6.23.3.7
horzcat
6.23.3.8
label
6.23.3.9
name
6.23.3.10
quantity
6.23.3.11
resolution
6.23.3.12
samplerate
Syntax:
• rate = samplerate(a)
samplerate returns samplerate of achse object.
6.23.3.13
scale
Syntax:
• r = scale(a,f)
Scale achses delta by factor f.
6.23.3.14
setdelta
Syntax:
• a = setdelta(a,f)
6.23.3.15
setfirst
Syntax:
• a = setfirst(a,f)
6.23.3.16
setname
Syntax:
• a = setname(a, newname)
6.23.3.17
setunit
Syntax:
• a = setunit(a,u)
87
6.23.3.18
setvalues
Syntax:
• a = setvalues(a, v)
6.23.3.19
spacing
Syntax:
• v = values(a, len)
Returns spacing values for linear, logarithmic or arbitary spacing in case of lin. or log. spacing. len
values are returned. In case of arbitary spacing, all stored values are returned.
6.23.3.20
unit
6.24
Class unit
6.24.1
Overview
Objects of class ’unit’ try to model physical units. It’s is possible to multiply or divide objects of this
type. A small database is used to find the right label for compound units.
See also : directory @unit/private, file units.mat
6.24.2
Attributes
• label - string
• name - string
• quantity - structure, holding two strings
• factor - double value
• exponents - vector
• dBScale - double value
• dBRef - double value
• opt - cell array, may be used to store optional information
6.24.3
Member functions
6.24.3.1
char
gives the unit’s label (e.g. V for Volt) back.
6.24.3.2
dbref
returns reference value for 0 dB when calculating decibel values from data of this unit.
88
6.24.3.3
dbscale
returns scaling value when calculating decibel values from data of this unit. dpscale returns either
10 (for power or energy units (e.g. Watt)) or 20 (for all other units (e.g. Volt).
6.24.3.4
display
6.24.3.5
double
gives a row vector which’s first element contains the unit’s factor and the remaining elements contain
the exponents of the SI basic units.
6.24.3.6
eq
6.24.3.7
exponents
returns dimension exponents of unit q.
6.24.3.8
factor
returns factor of unit q.
6.24.3.9
6.24.3.10
label
mpower
Syntax:
• mpower(u,p)
take unit u to power p, p must be a scalar.
6.24.3.11
mrdivide
6.24.3.12
mtimes
6.24.3.13
name
returns name of unit q.
6.24.3.14
quantity
returns quantity name of unit q. If argument which is omitted, the english quantity name will be
returned.
89
6.24.3.15
unit
unit class constructor
Class unit tries to modell physical units a physical unit is mainly can be described by the exponents
of the basic SI units, namely mass, length, time, current, temperature, luminal intensity, mole and
plane angle. Each unit belongs to a quantity, e.g. the unit s (second) is used when measuring the
quantity TIME. Each unit has a name, e.g. ’Ampere’, ’Volt’ , ’Joule’, ’hour’, and an abbreviation,
called label (’A’, ’V’, ’J’, ’h’). Unfortunately, the correspondence between these items is not always
bijectiv to find corresponding items, a table of units in the file units.mat is used.
A unit object can be created with different types of arguments:
• by giving the label: unit(’Hz’) looks up the remaining data (exponents, name, quantity) in the
table
• by giving the exponents
Some arithmetic can be done with units:
• units can be multiplied unit(’V’) * unit(’A’) = unit(’Watt’)
• or taken to an integer or rational power unit(’m’)2
6.25
Class list
6.25.1
Overview
Simple list of strings, used in class description (cf. Section 6.21).
6.25.2
Attributes
• data : cellarray of strings
• len : double value, counts number of strings in data
6.25.3
Member functions
6.25.3.1
append
Syntax:
• list = append(list, string)
• list = append(list, list)
Add string(s) to existing list.
6.25.3.2
cellstr
cellstr return cell array of strings from list l.
90
6.25.3.3
char
returns a char array from list l.
6.25.3.4
display
6.25.3.5
get
Syntax:
• s = get(l, nr)
returns string number nr from list l.
6.25.3.6
length
Syntax:
• len = length(l)
returns the number of strings in list l.
6.25.3.7
list
Syntax:
• l = list
creates empty list
• l = list(’Hello world’)
create list with one entry, ’Hello world’
• l = list(’Hello’, ’My’ , ’World’)
create list with three entries
• l = list(’Hello’, ’My’ , ’World’)
create list with three entries
An object of type list contains a list of strings.
6.25.3.8
sort
sort list l in increasing order.
91
Chapter 7
Frequently asked questions
7.1
Questions
1. Introduction and general information (cf. Section 7.2.1)
• What is TSTOOL ? (cf. Section 7.2.1.1)
• What software is required to run TSTOOL ? (cf. Section 7.2.1.2)
• On which systems does TSTOOL run ? (cf. Section 7.2.1.3)
• What about Octave or other Matlab like programming environments ? (cf. Section 7.2.1.4)
2. Installation of TSTOOL
• All lines in the OpenTSTOOL/tstoolbox/mex/*.m are comments, is this right? (cf. Section 7.2.2.1)
• Where are the precompiled Mex-Files? (cf. Section 7.2.2.2)
• There are more than one file called e.g. amutual.m, why? (cf. Section 7.2.2.3)
• What does the error message ”Attempt to execute SCRIPT . . . as a function.” mean? (cf.
Section 7.2.2.4)
• What does the error message ”This application has failed to start because the application
configuration is incorrect.” mean? (cf. Section 7.2.2.5)
3. Working with TSTOOL (cf. Section 7.2.3)
• How do I create a signal from my time-series data ? (cf. Section 7.2.3.1)
• How do I create a signal with logarithmic spacing ? (cf. Section 7.2.3.2)
• How do I create a signal from non-uniformly sampled data ? (cf. Section 7.2.3.3)
• How do I change the type of plot that I get with view ? (cf. Section 7.2.3.4)
• What is class ’signal’ for ? (cf. Section 7.2.3.5)
• What is class ’core’ for ? (cf. Section 7.2.3.6)
• What is class ’description’ for ? (cf. Section 7.2.3.7)
• What is class ’achse’ for ? (cf. Section 7.2.3.8)
• Why is class ’achse’ called ’achse’ and not ’axis’ ? (cf. Section 7.2.3.9)
• What is class ’unit’ for ? (cf. Section 7.2.3.10)
• How is class ’unit’ used in TSTOOL ? (cf. Section 7.2.3.11)
4. Extending TSTOOL (cf. Section 7.2.4)
93
• How can I write a script to automatize common tasks ? (cf. Section 7.2.4.1)
5. Miscellaneous questions (cf. Section 7.2.5)
• What’s the difference between history and commandlines ? (cf. Section 7.2.5.1)
• Is it TSTOOL, TSTool, OpenTSTOOL, OpenTSTool, ... ? (cf. Section 7.2.5.2)
6. Frequently encountered errors (cf. Section 7.2.6)
• Using a column vector to create a one-dimensional signal (cf. Section 7.2.6.1)
• What does the error message ”Attempt to execute SCRIPT . . . as a function.” mean? (cf.
Section 7.2.2.4)
7.2
Answers
7.2.1
Introduction and general information
7.2.1.1
What is TSTOOL ?
TSTOOL is a software package for nonlinear time series analysis, though it has a lot of features a
general signal analysis package would also have.
7.2.1.2
What software is required to run TSTOOL ?
TSTOOL is written in MATLAB, a powerful language for scientific computing, and in C++. Therefore you need MATLAB version 6.5 or higher to run tstool. Unfortunately, MATLAB is not free
software!
7.2.1.3
On which systems does TSTOOL run ?
TSTOOL should run on all platforms which run MATLAB and for which you can compile the included
mex-files, which are functions written in C or C++ that extend MATLAB’s set of build-in functions.
We try to ship pre-compiled mex-files with TSTOOL for the most popular operating systems, namely
Windows XP (32 and 64 bit), Linux (32 and 64 bit), Mac OS X and Solaris. However, since the
compiled mex-files are not compatible between all MATLAB versions are operating systems, you may
have to compile the mex-files yourself (see the installation section for details).
7.2.1.4
What about Octave or other Matlab like programming environments ?
Octave1 is a freely available language for scientific computing that strongly resembles MATLAB.
Unfortunately, Octave is not fully compatible to MATLAB, so TSTOOL does not work with it.
TSTOOL makes extended use of the object oriented features of MATLAB. In the current version of
Octave (3.0) there’s no full support of classes. Even if classes will be supported in future, it’s not sure
wheter TSTOOL will work properly.
There are several other Matlab like programming environments, e.g. Mideva2 or Scilab3 . Up to now,
it is not possible to use TSTOOL with these packages.
1 See
URL http://www.gnu.org/software/octave
URL http://www.mathtools.com
3 See URL http://www-rocq.inria.fr/scilab/
2 See
94
7.2.2
Installation of TSTOOL
7.2.2.1
All lines in the OpenTSTOOL/tstoolbox/mex/*.m are comments, is this right?
Yes, this are the comment-texts for the compiled mex functions (e.g. type help amutual at the
matlab prompt).
7.2.2.2
Where are the precompiled Mex-Files?
They are in OpenTSTOOL/tstoolbox/mex/<MEXEXT>, where <MEXEXT> is the extension for mex files on
your system. You can determine this extension by using the command mexext in Matlab.
7.2.2.3
There are more than one file called e.g. amutual.m, why?
For some functions there are up to three versions of the file:
• OpenTSTOOL/tstoolbox/@signal/amutual.m Function that invokes the underlying mex function. It uses signal objects as output and input.
• OpenTSTOOL/tstoolbox/mex/amutual.m Help text for the compiled mex function (e.g. type
help amutual on the matlab prompt).
• OpenTSTOOL/tstoolbox/mex/mexsol/amutual.mexsol,
OpenTSTOOL/tstoolbox/mex/mexsg64/amutual.mexsg64,
OpenTSTOOL/tstoolbox/mex/mexglx/amutual.mexglx,
OpenTSTOOL/tstoolbox/mex/mexw32/amutual.mexw32
Precompiled mex files for Linux x86, Windows, Mac OS X and Solaris are shipped with TSTOOL. Only one of these files may be present on your system, depending on the version of
TSTOOL you have downloaded.
7.2.2.4
What does the error message ”Attempt to execute SCRIPT . . . as a function.”
mean?
Matlab cannot find the correct mex files for this systems and so it tries to execute the scripts OpenTSTOOL/mex/*.m (which are only the help texts for the mex files). There are many possibilities for
this error:
• You downloaded the wrong version of TSTOOL.
• The path setting made by settspath.m are not correct. Type path at the matlab prompt and
look for the path setting for the mex directory (see 7.2.2.3).
• The mex files are not present in the directory noted in 7.2.2.3.
7.2.2.5
What does the error message ”This application has failed to start because the
application configuration is incorrect.” mean?
This happens on Windows systems without the Visual C++ 2008 run-time libraries. Since the mexfiles for Windows are compiled with VC++ 2008, these run-time libraries are needed for the proper
execution of the compiled Windows mex-files that ship with TSTOOL. Please see the installation
section for details on how to install the run-time libraries.
95
7.2.3
Working with TSTOOL
7.2.3.1
How do I create a signal from my time-series data ?
Suppose the time-series data is given as the row vector y.
>> s = signal(y)
>> view(s)
If y is a column vector, the following syntax must be used:
>> s = signal(y’)
>> view(s)
Suppose the data was recorded with a samplerate of 8 kHz :
>> s = signal(y, 8000)
>> view(s)
7.2.3.2
How do I create a signal with logarithmic spacing ?
Suppose you have data vector y whose values were recorded at 3 Hz, 6 Hz, 12 Hz, 24 Hz ...
a = achse(unit(’Hz’), 3, 2, ’log’)
s = signal(y, a)
view(s)
7.2.3.3
How do I create a signal from non-uniformly sampled data ?
Suppose you have a data vector y (of length 4) whose values were recorded at 3 Hz, 5 Hz, 8 Hz, 14.5
Hz
a = achse(unit(’Hz’), [3 5 8 14.5])
s = signal(y, a)
view(s)
7.2.3.4
How do I change the type of plot that I get with view ?
The way view plots a signal depends on the attributes of the signal. It is possible to give view a hint
which type of plot to prefer. This hint can be set with the command setplothint. The possible plot
types can be obtained by issuing
help signal/view
at the Matlab prompt. However, if the signal does not support the desired type of plotting (e.g. a
one-dimensional time-series can not be visualized as orbit), view will use the default plot type for the
data.
s = signal(rand(1000, 3));
s = setplothint(s, ’3dpoints’);
view(s)
96
7.2.3.5
What is class ’signal’ for ?
Class signal is TSTOOL’s main class. Objects of this type model real world signals. A signal does not
only store the pure sample values, it holds much more information like axes, units of sample values
or the axes units, and even more descriptive information like labels, command lines and a processing
history.
The majority of functions in the tstoolbox take a signal as input argument and return a processed
signal as output. This allows for combining or chaining of several processing steps in order to get the
desired output.
7.2.3.6
What is class ’core’ for ?
Class core is a base class of class signal. An object of type core stores the pure sample values of
a signal, without any additional descriptive information. The separation of the numerical and the
descriptive part of a signal simplifies the writing of m-files that work on signals.
7.2.3.7
What is class ’description’ for ?
Class description is the second base class of class signal. An object of type description stores all
descriptive information belonging to a signal.
7.2.3.8
What is class ’achse’ for ?
Class achse models an axis, e.g. a time axis or a frequency axis. A signal has a least one axis (if it is a
one dimensional signal). A multidimensional signal has several achse objects, one for each dimension.
An achse object is basically described by an object of class unit and the spacing values. The spacing
may be linear, logarithmic or arbitrary (in case of non-uniform sampling).
7.2.3.9
Why is class ’achse’ called ’achse’ and not ’axis’ ?
The names axis and axes are already occupied in Matlab. So, achse, which is the german translation
of axis, was used as name for that class.
7.2.3.10
What is class ’unit’ for ?
Objects of class ’unit’ try to model physical units. No one wonders that his computer can multiply
real or complex numbers. But in physics or engineering, you also have to mulitply or divide physical
units, just think of Ohm’s law : R = U/I
7.2.3.11
How is class ’unit’ used in TSTOOL ?
Class unit is used as a part of every achse object and as part of a description object. Handling
and processing of units is optional for functions that work on signals, because many nonlinear signal
analysis functions do not allow consistent handling of units.
7.2.4
Extending TSTOOL
Of course it’s possible to extend TSTOOL with some custom functionality or to use parts of TSTOOL
in your own m-files, just as with other toolboxes for Matlab.
97
7.2.4.1
How can I write a script to automatize common tasks ?
One way to obtain a script is to execute the desired analysis steps with one example signal. The
output of this tasks will again be a signal that has stored the syntax of the executed steps in its
description. Using the command
commandlines(result)
will give you this syntax. With copy and paste, it’s possible to create a script file from that output.
7.2.5
Miscellaneous questions
7.2.5.1
What’s the difference between history and commandlines ?
Both attributes of class description are used to record the processing history of a signal. But, while
history contains a list human readable entries, commandlines stores the exact syntax of the commands
that were applied to the signal.
7.2.5.2
Is it TSTOOL, TSTool, OpenTSTOOL, OpenTSTool, ... ?
Initially it was called TSTOOL, but since Matlab now has its own tstool command, we changed
the Matlab command to opentstool, but keep mostly TSTOOL in the manual and homepage for
brevity’s sake. Regarding the spelling, we’re not entirely sure, either.
7.2.6
Frequently encountered errors
7.2.6.1
Using a column vector to create a one-dimensional signal
TSTOOL stores one-dimensional signals always as row vectors. Giving a column vector will cause
unexpected behaviour with most routines that process signals:
>> s = signal(sin(0:0.5:100))
s = signal object
Dlens : 1 201
X-Axis 1 : |
X-Axis 2 : |
Name :
Type :
Attributes of data values :
|
Comment :
History :
16-Aug-1999 19:15:01 : Imported from MATLAB workspace
Instead, a row vector must be given to create the desired one-dimensional signal:
98
>> s = signal(sin(0:0.5:100)’)
s = signal object
Dlens : 201
X-Axis 1 : |
Name :
Type :
Attributes of data values :
|
Comment :
History :
16-Aug-1999 19:16:58 : Imported from MATLAB workspace
99
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